# 9.7: Factoring Polynomials Completely

Difficulty Level: 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 a1\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 (x24)(x2+1)\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

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