Practice Factoring Polynomials by Grouping

Factoring Common Binomials

Work through example 3, Factoring by Grouping, and solve the problems 11 to 15, 17, 18, and 23–27 in the practice set. All of these problems are four-term polynomials that you can factor by grouping. After you have completed the practice problems, check your answers against the answer key.

The first step in the factoring process is often factoring the common monomials from a polynomial. Sometimes polynomials have common terms that are binomials. For example, consider the following expression.

\(\begin{align*}x(3x+2)-5(3x+2)\end{align*}\)

You can see that the term \(\begin{align*}(3x+2)\end{align*}\) appears in both terms of the polynomial. This common term can be factored by writing it in front of a set of parentheses. Inside the parentheses, we write all the terms that are left over when we divide them by the common factor.

\(\begin{align*}(3x+2)(x-5)\end{align*}\)

This expression is now completely factored. Let's look at some examples.

Example 2

Factor \(\begin{align*}3x(x-1)+4(x-1)\end{align*}\).

Solution:

\(\begin{align*}3x(x-1)+4(x-1)\end{align*}\) has a common binomial of \(\begin{align*}(x-1)\end{align*}\).

When we factor the common binomial, we get \(\begin{align*}(x-1)(3x+4)\end{align*}\).