Unit 8: Operations with Polynomials
Polynomials are a special type of algebraic expression that contain two or more terms. For example, a polynomial might look like 5x + 2x3 + x2 + 2. In this unit, we discuss how to recognize, classify, add, subtract, multiply, and divide polynomials by combining like terms and using the distributive property. These skills help us make calculations that pertain to the motion of two or more objects. For example, we can calculate when and where a runner will overtake a competitor, or how much interest you will earn from two or more savings accounts.
Completing this unit should take you approximately 4 hours.
8.1: Classifying Polynomials
When we discuss polynomials, we are referring to an algebraic expression that includes more than one term. We classify polynomials based on the number of terms in the expression.
8.2: Adding and Subtracting Polynomials
Like all mathematical expressions, we can perform basic mathematical operations on polynomials. In this section we learn how to add and subtract polynomials using different common methods.
8.3: Multiplying a Polynomial by a Monomial
We can multiply polynomials by monomials or other polynomials. In this section, we will see how to multiply a polynomial by a monomial. We can use the distributive property to do this.
8.4: Multiplying Binomials (FOIL)
When multiplying two binomials (polynomials with two terms), we cannot simply use the distributive property. We need to ensure that each term in one binomial is multiplied by each term in the other binomial. The technique we use to do this is called FOIL. FOIL is a mnemonic that stands for First, Outer, Inner, Last. When we place two binomials next to each other, FOIL reminds us of the order we multiply the terms in.
8.5: Complete the Square and Difference of Two Squares
We sometimes need to take the square of a binomial. In this section, we will look at the specific rules for squaring binomials. These rules are derived from the FOIL method.
8.6: Multiplying Polynomials with Any Number of Terms
Polynomials can have more than two terms, and we will need to know the methods for multiplying these larger polynomials.
8.7: Dividing a Polynomial by a Monomial
We also need to be able to divide polynomials. In this section, we will review some techniques for dividing a polynomial by a monomial.
8.8: Dividing a Polynomial by a Binomial
The last mathematical operation we need to discuss is dividing polynomials by binomials.