# 9.7: Factoring Polynomials Completely

**At Grade**Created by: CK-12

## Learning Objectives

At the end of this lesson, students will be able to:

- Factor out a common binomial.
- Factor by grouping.
- Factor a quadratic trinomial where \begin{align*}a \neq 1\end{align*}.
- Solve real-world problems using polynomial equation.

## Vocabulary

Terms introduced in this lesson:

- factoring strategy
- factor completely
- recognize special products
- common monomial
- factor by grouping

## Teaching Strategies and Tips

Have students learn the four strategies for completely factoring a polynomial provided in the introduction.

Use Examples 3-5 to show a new factoring technique called “factoring by grouping.”

Knowing when a polynomial is completely factored may be difficult to some students. Suggest that they check each factor to see if it can be factored any more. For example, a polynomial such as \begin{align*}(x^2 - 4)(x^2 + 1)\end{align*} is not completely factored.

Factoring is easier when the leading term has a positive coefficient. Suggest that students include the negative as part of the GCF right in the beginning.

## Error Troubleshooting

NONE