MA001: College Algebra

Please read section 0.3 to learn about order of operations. The assignment listed under this subunit corresponds to this reading. Mathematics would be useless if some people thought 3 + 4 x 2 = 14 and others thought 3 + 4 x 2 = 11. Understanding the order of operations is the most basic (and important) task of the student of mathematics.

Please complete pages 4 to 5 of Wallace's workbook to learn about order of operations. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Remember that the primary rule for order of operations is that things in parentheses be simplified first.

Watch the first  video, which introduces you to the order of operations. Please pay attention to the order in which operations are used and the mnemonic PEMDAS and what it stands for. Note that the video does not make use of the equal sign. Please take a look at Saylor Academy's "Revision to MA001 Video" for a detailed explanation of how to solve the two problems presented in the video.

Then, watch the second video. In this video, you will apply PEMDAS to solving problems by first removing parentheses, simplifying exponents, multiplying, dividing, adding, and subtracting. Please understand that regarding multiplication and division, we perform whichever comes first, from left to right.

Complete page 7 of Wallace's workbook to apply your knowledge about order of operations with absolute values. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Absolute values tell us how far apart two numbers are, and we need to practice working with absolute value equations.

Watch this video, paying attention to the examples being used to explain the concept of absolute values. You may refer to the video when doing your homework, if necessary.

Watch this brief video. Pay attention to the examples being used to explain the concept of four operations on integers. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 6 of Wallace's workbook to practice with the four operations on integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Fractions allow us to manipulate complicated expressions that include division. Being able to work with fractions allows us to simplify (and often avoid) division.

Review the topics covered in the course so far, and then complete these exercises. Answer only the odd-numbered questions in numbers 1 to 25.

Read this section to learn how to evaluate algebraic expressions for some given values.

Complete page 8 of Wallace's workbook to evaluate algebraic expressions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this brief video, which discusses how to evaluate expressions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 9 of Wallace's workbook for practice with combining like terms. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this brief video, paying attention to the examples do the practice problem set on to access your understanding. You may watch the video as often as you please. You may refer to the video when doing your homework if necessary.

Complete page 10 of Wallace's workbook for practice with simplifying algebraic expressions, using the distributive property. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this brief video. Note that when we distribute, we take into consideration the sign of the number we are distributing. Particularly, if you distribute a negative number over a positive number you get a negative number and vice versa. Be careful when you distribute negative numbers. 

Complete page 11 of Wallace's workbook for practice with distributing and combining like terms. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this brief video. As we have already familiarized ourselves with distribution in subunit 1.2.3 above, this lesson will expand on that to combine like terms. The goal here is to be able to distribute and combine terms that are alike: terms with the same variable or group of variables and exponents. Remember that combining like terms is simply adding or subtracting the numerical coefficients in the like terms.

Review the topics covered above, watch the videos, and then do the exercises provided in the link above. Answer every other odd question in 1-81.

Watch this brief video. Note that the take-home message here is that in linear equations, and in other equations you will handle in the future, we can add and multiply same expressions on both sides of the equation. We must do the same thing to each side in order to keep the balance, otherwise we change the solutions to our problem.

Read this section, beginning on page 28, to learn how to solve "one step equations."

Complete page 12 of Wallace's workbook for practice with solving one step linear equations.

Read section 1.2 on page 33 to learn how to solve "two step equations." Note that the assignment at the end of this subunit corresponds with this reading.

Complete page 13 of Wallace's workbook for practice with solving two step linear equations. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this video to learn how to solve two-step equations. You may watch the video as often as you please. You may refer to the video when doing your homework if necessary.

Watch this brief optional video if you feel like you need additional help with this topic.

Read this section, beginning on page 37, to learn how to solve general linear equations.

Watch this brief optional video if you feel like you need additional help with this topic.

Complete page 14 of Wallace's workbook for practice with simplifying general linear equations with one variable. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions. Note that the video contains a small error in its discussion of Practice B, which will affect the final answer.

Watch this brief video, paying attention to the examples being used to explain how to solve general linear equations with one variable. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary. Please note that there is a small math error at the 3:15-minute mark in the video; the 5 is not distributed correctly on the right side. The correct answer to the example is -6. For a full explanation of how to solve the problem, please read the "Revision to Tyler Wallace's 'Linear Equations in One Variable'".

Read this section, beginning on page 43, to learn how to solve equations involving fractions.

Complete pages 15 and 16 of Wallace's workbook for practice with solving equations with fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

The first video demonstrates how to solve equations that involve fractions. The second explains how to distribute fractions in linear equations that have one variable. You may watch the videos as often as you please. You may refer to the videos when doing your homework, if necessary.

Watch these brief optional videos if you feel like you need additional help with this topic.

Answer every other odd-numbered problem in questions 1 through 39.

Answer every other odd-numbered problem in questions 1 through 49.

Answer every other odd-numbered problem in questions 1 through 29.

Read this section. You now have the skills to take a formula that relates two or more quantities and solve it for whichever quantity you want. Notice how this allows us to use formulas in many ways. This is also great practice for algebra skills we will use throughout the course.

Complete page 17 of Wallace's workbook for practice with two-step formulas. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this brief video, paying attention to the examples being used to explain two-step formulas. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 18 of Wallace's workbook for practice with multi-step formulas. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this brief video, which explains how to use multistep formulas. Also, note that the four properties you studied earlier in this course are also applicable here. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 19 of Wallace's workbook for practice with clearing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, paying attention to the examples being used to explain how to clear fractions when using formulas. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Review the topics, watch the videos, and do the exercises provided in the link above. Answer the odd-numbered questions from 1 to 49. Solutions are given on page 2 of the PDF.

Read this section. The equations x - 3 = 2 and |x - 3| = 2 are very different from each other, but they are also closely. Notice how we turn an equation with absolute values into two equations without absolute values. Note that this reading covers all the material you need to know for subunits 1.5.1-1.5.3.

Complete page 20 of Wallace's workbook to practice solving absolute value equations with two solutions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, which explains how two solutions are applied to absolute value equations. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 21 of Wallace's workbook for practice with isolating absolute values. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions. (Note that the final term in Example B in the workbook should be -31 rather than -32).

Watch this five-minute video, paying attention to the examples being used to explain how to isolate an absolute value. Watch the video as many times as necessary to understand the concept. You may refer to the video when doing your homework, if necessary.

Watch this five-minute video, which demonstrates how to solve absolute value equations when two absolute values are involved. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 22 of Wallace's workbook to practice solving for variables with equations that contain two absolute values.

Review the topics covered in the course so far, and then complete the exercises linked above. Work on only the odd-numbered questions for numbers 1 through 35. Solutions are given on page 2 of the PDF.

Read this section. Word problems are about gathering information, turning it into equations, and then using the equations to solve the stated problem. Please focus on the various ways that we turn English statements into mathematical equations.

Watch this five-minute video, paying attention to the examples being used to learn how to translate words into mathematical expressions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 23 of Wallace's workbook to apply your knowledge of consecutive even and odd integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, paying attention to the examples being used to learn how to solve problems with consecutive integers. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 24 of Wallace's workbook to practice solving word problems with consecutive integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Complete page 25 of Wallace's workbook to apply your knowledge of consecutive even and odd integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, which shows how to solve problems with consecutive even and odd integers. You may watch the video as often as you please. You may refer to the video when doing 

Complete page 26 of Wallace's workbook to practice solving word problems that involve angles of triangles. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, which explains how to solve problems using angles of triangles. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 27 of Wallace's workbook to practice solving word problems involving perimeters. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, paying attention to the examples that explain how to problem solve with the perimeter of rectangles. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Review the topics covered so far in this course, and attempt the odd numbered exercises in questions 1 to 45. Solutions are on page 4 of the PDF.

Read this section.

Complete page 28 of Wallace's workbook to practice solving word problems that ask you to solve for a person's age. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, which demonstrates how to solve age problems. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Watch these brief optional videos if you feel like you need additional help with this topic.

Watch this five-minute video, paying attention to the examples being used to further explain how to solve age problems. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete pages 29 and 30 of Wallace's workbook to practice solving word problems to determine ages of a person in the past based on information given about the person's age now.

Watch this brief optional video if you feel like you need additional help with this topic.

Answer the odd numbered problems for questions 1 to 39. Solutions are on page 4 of the PDF.

Review Unit 1 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. This is very important. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, check your answers against Saylor Academy's "Unit 1 Practice Test - Answer Key".

Read this section. Note the difference in meaning among "equal," "less than," and "less than or equal," and the symbols we use for these ideas. Focus on how the steps for solving inequalities are different than for solving equations.

Watch this four-minute video, paying attention to the examples being used to explain graphing inequalities. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary. In this unit, the operations on the terms are very similar to solving equations. Here, we make use of inequality instead of an equal sign. The inequality sign switches/flips when you multiply or divide both sides by a negative number.

Complete page 32 of Wallace's workbook to practice graphing inequalities on a number line. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these brief optional videos if you feel like you need additional help with this topic.

Complete page 33 of Wallace's workbook to practice with interval notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

We use plots, graphs, and pictures to help us understand and communicate. Interval notation is a very visual way to communicate inequalities, and it also gives us visual techniques for solving them.

Watch this three-minute video, paying attention to the examples being used to explain interval notation. Note when to use a square bracket and a round bracket. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Watch this brief optional video if you feel like you need additional help with this topic.

Complete page 34 of Wallace's workbook to practice solving inequalities. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, paying attention to the examples which provide a linear approach to solving inequalities. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Watch this five-minute video. Note that compound or tripartite inequalities are very similar to linear inequalities, except for the way they are structured. Bear in mind that in the tripartite inequalities, we will be balancing the left center and right. This means whatever you decide to do to the center in order to get the variable in question by itself, you have to do the same to the other two parts of the inequality. Notice also that if you divide or multiply through by a negative number, then you have to flip the inequality signs.

Complete page 35 of Wallace's workbook to practice solving inequalities. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Answer odd-numbered problems 1 to 37.

Answer all problems, from 1 to 19.

Read this section, on pages 89 to 93. One of our most powerful tools is visualization; graphs and XY coordinates comprise the foundation of "seeing" math. Getting comfortable when working with points and lines in a coordinate system is the main point of this section.

Read the following short article for a brief description of the four quadrants of a Cartesian graph.

Complete page 36 of Wallace's workbook for practice with graphing based on points provided or equation of the line provided. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, which discusses points and lines in graphing and slopes. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Watch this brief optional video if you feel like you need additional help with this topic.

Read this section, which focuses on one fundamental property of the line: its slope. The slope tells us how much the line rises as we move to the right. There are several ways to talk about this one idea.

Complete page 37 of Wallace's workbook to work on determining the slope of a line, given the line on a graph. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video, paying attention to the examples being used to explain the slope of a graph. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 38 of Wallace's workbook to work on finding the slope when given two sets of points. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video. Take note of the examples used in the video to explain how to find the slope using two points on the graph. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Watch this brief optional video if you feel like you need additional help with this topic.

Work through problems 1, 2, and every other odd problem from question 3 through 21.

Attempt the odd problems from questions 1 through 29.

Read this section. We know what a line is when we see it plotted. There is more than one useful way to write the equation for a line.

Complete page 39 of Wallace's workbook to practice providing the slope intercept equation when given information of the slope and y-intercept, or a graph. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video to learn about the slope-intercept equation and its applications. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Watch this brief optional video if you feel like you need additional help with this topic.

Complete page 40 of Wallace's workbook to practice putting an equation in intercept form. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video to learn about putting equations in intercept form. Understand that sometimes there will be no intercept or slope, in which case the slope or intercept will be zero.

Complete page 41 of Wallace's workbook to work on graphing equations. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, paying attention to the examples being used to instruct you on how to graph equations. Be sure that you understand the different parts of the straight line equation and the names that go with them. You may practice by graphing your own lines and seeing if you can label them completely.

Complete page 42 of Wallace's workbook to practice graphing or finding the equations for vertical and horizontal lines. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this two-minute video, which discusses the different characteristics of vertical and horizontal lines. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 43 of Wallace's workbook to practice finding the point slope equation, given a point the line passes through and the slope. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, paying attention to the examples being used to demonstrate the point-slope equation.

Watch this brief optional video if you feel like you need additional help with this topic.

Complete page 44 of Wallace's workbook to practice with finding an equation when given two points. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, focusing on the examples used to find the equation of the line with two points given.

Answer every other odd-numbered problem in questions 1 through 41.

Answer every other odd-numbered problem in questions 1 through 51.

Read this section. Parallel lines never intersect, which is good to know if you are looking for an intersection! The shortest distance from a line to something else is perpendicular to the line. The slopes for parallel and perpendicular lines have simple relationships to each other (which you should memorize!).

Watch this brief optional video if you feel like you need additional help with this topic.

Complete page 45 of Wallace's workbook to practice determining whether lines will be parallel, perpendicular, or neither. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, focusing on the examples used to explain how to find the slope of parallel and perpendicular lines. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 46 of Wallace's workbook to find the equations of parallel and perpendicular lines. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video to learn about equations used for parallel and perpendicular lines.

Answer the odd-numbered problems for questions 1 through 47.

Read this section. The relationship among distance, rate, and time is one of the simplest and most fundamental of physics and engineering. Notice how d = rt is a relationship that can be solved for any of the three variables.

Complete page 47 of Wallace's workbook to practice solving distance problems. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, which demonstrates how to solve distance problems involving opposite directions. In working with distance and rate problems, it will be helpful if you begin every question by first drawing a picture and translating the picture into a table as demonstrated in the video. Finally, apply the formula to get the required answer. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 48 of Wallace's workbook to practice solving distance problems. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Two objects may be moving in the same direction or in different directions. This is the simplest relationship between two moving objects. "Catch-Up" problems are about moving in the same direction but at different speeds.

Watch this five-minute video, which demonstrates distance problems in which one person is trying to catch up with another person. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 49 of Wallace's workbook to practice solving distance problems. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, paying attention to the distance and rate problems shown to demonstrate the concept of total time. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Answer the odd-numbered problems for questions 1 through 37.

Review Unit 2 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the "Unit 2 Practice Test - Answer Key".

Read this section. Polynomials are all about adding and multiplying powers of x. Notice that we have specific rules that govern multiplying and dividing powers of x and raising a power of x to another power.

Complete page 51 of Wallace's workbook to practice implementing the product rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this three-minute video, which discusses the product rule for exponents.

Complete page 52 of Wallace's workbook to practice implementing the quotient rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these two videos, which discuss the quotient rule for exponents.

Complete page 53 of Wallace's workbook to practice implementing the power rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these two videos, which discuss the power rule for exponents.

Read this section. Notice that a negative exponent in the denominator is the same as a positive exponent in the numerator. Conversely, a negative exponent in the numerator is the same as a positive exponent in the denominator.

Complete page 54 of Wallace's workbook to practice with the zero power rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video, which discusses the zero power rule with exponents. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 55 of Wallace's workbook to practice with negative exponents. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these two videos, which discuss rules for negative exponents.

Watch this video, which shows a short proof of the zero exponent.

Complete page 56 of Wallace's workbook to solve equations using the properties of exponents. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch each of these videos, focusing on the examples used that demonstrate how to simplify exponents with the properties and rules you have learned so far, i.e., product rule, quotient rule, etc.

Answer the odd-numbered problems for questions 1 through 43.

Answer the odd-numbered problems for questions 1 through 39.

Read this section. Scientific notation allows us a general idea of the size of a number with a glance at the exponent, instead of counting places before or after a decimal point.

Complete page 57 of Wallace's workbook to practice with converting between standard and scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, which demonstrates how to convert between standard and scientific notation.

Complete page 58 of Wallace's workbook for more practice with scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video, paying attention to the examples being used to further explain scientific notation. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 59 of Wallace's workbook for more practice with scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this three-minute video, which discusses how to multiply and divide with scientific notation.

Complete page 60 of Wallace's workbook to practice with multiplying and dividing scientific notation with a result that is not in scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video, which addresses multiplication and division and then converting the answer to scientific notation.

Answer the odd-numbered problems for questions 1 through 41.

Read this section. Evaluating a polynomial is simply plugging in a value for the variable and then simplifying.

Watch this five-minute video, which provides definitions and characteristics of polynomials and gives examples of evaluating polynomials.

Complete page 62 of Wallace's workbook to practice adding and subtracting polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video, paying attention to the examples being used to add and subtract polynomials.

Read this section. Multiplying polynomials is all about being careful with distribution (focus on how parentheses are used to make sure we distribute correctly) and following the rules for exponents (focus on how we use x_p x_q = x_p+q). 

Complete page 63 of Wallace's workbook to practice multiplying by monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this three-minute video, paying attention to the examples being used to explain how to multiply by monomials.

Complete page 64 of Wallace's workbook to practice multiplying by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video, paying attention to the explain of how to multiply binomials.

Complete page 65 of Wallace's workbook to practice multiplying by trinomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, paying attention to the explanation of how to multiply trinomials.

Complete page 66 of Wallace's workbook to practice multiplying monomials by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video, paying attention to the examples being used to explain how to multiply monomials by two binomials.

Read this section. The idea of this section is to point out a few nice and important special cases of polynomial multiplication. Memorize these special products and it will pay off big later!

Complete page 67 of Wallace's workbook to practice multiplying monomials by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, paying attention to the examples used to explain sums and differences with polynomials.

Complete page 68 of Wallace's workbook to practice with perfect squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss the perfect square shortcut.

Answer every other odd numbered problem for questions 1 through 41.

Answer every other odd numbered problem for questions 1 through 39.

Answer every other odd numbered problem for questions 1 through 39.

Read this section. Dividing polynomials is just the same as the long division you learned in elementary school. It is also great practice in solidifying your skills in exponents and multiplication. Pay special attention to how the exponents work as place holders just as the digits in the 1s, 10s, 100s, and so forth, places did for us in elementary school.

Complete page 69 of Wallace's workbook to practice dividing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss division by monomials.

Complete page 70 of Wallace's workbook to practice dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Complete page 71 of Wallace's workbook for more practice with dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, paying attention to the examples used to explain the division of polynomials. You may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.

Answer odd-numbered problems for questions 1 through 43. Keep in mind that you are allowed to watch the videos as often as you please to help you answer the homework problems.

Review Unit 3 before clicking on the link above to take the practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the "Unit 3 Practice Test - Answer Key". 

Read this section. Pay special attention to page 212.

Complete page 73 of Wallace's workbook to practice finding the greatest common factor. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this two-minute video, which discusses how to find the Greatest Common Factor (GCF). You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 74 of Wallace's workbook to practice factoring the greatest common factor. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos to learn how to factor the Greatest Common Factor (GCF).

Read this section. Pay special attention to page 216.

Complete page 75 of Wallace's workbook to practice factoring the greatest common factor. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss the GCF and grouping methods. You may watch the videos as often as you please. You may refer to the videos when doing your homework, if necessary.

Complete pages 76 and 77 of Wallace's workbook to practice with grouping and order change. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, paying attention to the examples being used to explain grouping with order change. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

You may take different steps than in the video - or even more steps - but please make sure that you get the same result and that you understand the steps taken in the video.

Answer every other odd-numbered problem for questions 1 through 31.

Answer every other odd-numbered problem for questions 1 through 27.

Read this section. Pay special attention to page 221.

This method of factoring (the ac method) really is the workhorse of factoring trinomials: We need two numbers whose product is the constant term and whose sum is the x coefficient.

Complete page 80 of Wallace's workbook to practice with trinomials when a = 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, paying attention to the examples used to explain how to factor trinomials when a is equal to 1. You may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 81 of Wallace's workbook for more practice with trinomials when a = 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video for a continuation of the video that explains how to factor trinomials when a is equal to 1.

Read this section. When we multiply polynomials we are distributing across parentheses. Here we are doing the reverse: We are trying to write a polynomial as a product of factors. We will introduce several techniques, and you should focus on learning them all because later it will be up to you to match the correct technique to a given problem.

Complete page 78 of Wallace's workbook for practice with trinomials when a ≠ 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video. Pay attention to the examples used to describe how to factor trinomials when the leading coefficient is not 1. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 79 of Wallace's workbook for more practice with trinomials when a ≠ 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video, paying attention to the examples being used to explain the concept in this unit.

Watch this four-minute video. Pay attention to the examples being used to explain the concept in this unit. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Answer the odd-numbered problems 1 to 25.

Answer the odd-numbered problems 1 to 39.

Read this section. There is an error in Exercise 308 on page 231. You can find the correction in Saylor Academy's "Correction to Exercise 308, Page 231".

Complete page 82 of Wallace's workbook to reinforce your understanding of differences of squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss the difference of squares.

Complete page 83 of Wallace's workbook to reinforce your understanding of sum of squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this two-minute video, which discusses the sum of squares. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 84 of Wallace's workbook to reinforce your understanding the difference of 4th powers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video, which addresses how to use fourth powers. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 85 of Wallace's workbook for practice with perfect squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss perfect squares and perfect square trinomials.

Complete page 86 of Wallace's workbook to practice with cubes. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which explain the concept of cubes.

Complete page 87 of Wallace's workbook for practice with the greatest common factor in terms of special products. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this three-minute video, paying attention to the examples being used to explain the concept of special products with the GCF. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Answer all of the odd-numbered problems for questions 1 through 47.

Read this section. Pay special attention to page 234. Note that this reading corresponds to the workbook assignment at the end of this subunit.

Complete page 88 of Wallace's workbook to reinforce your knowledge of when to use certain methods of factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss factoring strategies. You may watch the videos as often as you please. You may refer to the videos when doing your homework, if necessary.

Read this section. Here we emphasize how we can solve problems by factoring. Focus on the rule - "if ab = 0, then a = 0 or b = 0 (or both)" - and how factoring makes this rule so important.

Read this section. Here we emphasize how we can solve problems by factoring. Focus on the rule - "if ab = 0, then a = 0 or b = 0 (or both)" - and how factoring makes this rule so important.

Complete page 89 of Wallace's workbook to reinforce your knowledge of the zero product property. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which explain the zero product rule.

Complete page 90 of Wallace's workbook for practice with factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video. Pay attention to the examples to demonstrate how to solve by factoring.

Complete page 91 of Wallace's workbook for practice with factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video. Pay attention to the examples being used to explain how to factor by making the equation equal zero.

Complete page 92 of Wallace's workbook for practice with simplifying and factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, focusing on the examples that discuss how to simplify equations. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Answer all of the odd-numbered problems for questions 1 through 35.

Review Unit 4 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the "Unit 4 Practice Test - Answer Key".

Read this section. Rational expressions are just fractions and fractions of polynomials. Focus on the use of the rules of exponentiation and when we can cancel in fractions.

Complete page 94 of Wallace's workbook for practice with reducing rational expressions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this four-minute video. Pay attention to the examples being used to explain evaluate rational expressions.

Complete page 95 of Wallace's workbook for practice with reducing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this two-minute video. Pay attention to the examples being used to explain the concept of reducing fractions in rational expressions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 96 of Wallace's workbook for practice with reducing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos. Pay attention to the examples used to explain the concepts in this unit.

Complete page 97 of Wallace's workbook for practice with reducing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss how to reduce polynomials.

Answer all of the odd-numbered problems for questions 1 through 49.

Read this section. Again, rules for exponents are paramount, but now focus on dividing as "inverting and multiplying."

Complete page 98 of Wallace's workbook for practice with multiplying and dividing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which show how to multiply and divide fractions.

Complete page 99 of Wallace's workbook for practice with multiplying and dividing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss the multiplication and division of monomials.

Complete page 100 of Wallace's workbook for practice with multiplying and dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Complete page 101 of Wallace's workbook for practice with multiplying and dividing polynomials both at once. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss the multiplication and division of polynomials. Remember that you may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.

Watch these videos if you feel like you need additional help with this topic. These videos demonstrate how to solve variations on this kind of problem. 

Answer all of the odd-numbered problems for questions 1 through 43.

Read this section. One of the skills students have most difficulty with is adding fractions. You can make this much easier by understanding least common denominators.

Complete page 102 of Wallace's workbook for practice with the Lowest Common Denominator (LCD). Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss the Least Common Denominator (LCD). You may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 103 of Wallace's workbook for more practice with Lowest Common Denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch these videos, which discuss the Least Common Denominator with monomials.

Complete page 104 of Wallace's workbook for more practice with Lowest Common Denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, which discusses the Least Common Denominator with polynomials.

Answer questions 11-20. If necessary, use the videos and information in this subunit to help you solve these problems.

Read this section and complete the corresponding workbook assignment for this subunit. Notice that most of the work involves finding a common denominator; once that is done, we simply need to be careful with multiplication.

Complete page 105 of Wallace's workbook for practice with adding and subtracting fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video. Pay attention to the examples being used to explain how to add and subtract fractions.

Read this section and complete the corresponding workbook assignment for the subunit.

Complete page 106 of Wallace's workbook for practice with adding and subtracting common denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video. Pay attention to the examples used to explain adding and subtracting when there are different denominators. Here, one would first obtain a common denominator for the expressions involved and then proceed as in subunit 5.4.2.1 above.

Complete page 107 of Wallace's workbook for practice with adding and subtracting different denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video which discusses adding and subtracting when there are different denominators. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Answer the odd-numbered problems for questions 1 through 43.

Read this section and complete the corresponding workbook assignment for this subunit. Notice how converting from minutes to hours or feet to miles or cups to gallons all have the same foolproof method: canceling units of measurement.

Complete page 108 of Wallace's workbook for practice with dimensional analysis in which you convert single units. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video which discusses converting single units. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Complete page 109 of Wallace's workbook for practice with dimensional analysis with converting dual units. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Watch this five-minute video, which discusses converting dual units.

Answer all of the problems.

Review Unit 5 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the "Unit 5 Practice Test - Answer Key".