# 9.4: Polynomial Equations in Factored Form

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

## Learning Objectives

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

- Use the zero-product property.
- Find greatest common monomial factor.
- Solve simple polynomial equations by factoring.

## Vocabulary

Terms introduced in this lesson:

- factoring, factoring a polynomial
- expanded form
- factored form
- zero product property
- factoring completely
- common factor
- greatest common monomial factor
- polynomial equation

## Teaching Strategies and Tips

Use the introduction to motivate factoring.

- The reverse of distribution is called factoring.
- Whereas before students were learning the direction
(a+b)(x+y)⇒ax+bx+ay+by ; they will now learn to “put it back together”:ax+bx+ay+by⇒(a+b)(x+y) . - Students realize that polynomials can be expressed in expanded or factored form

Teachers may decide to have their students pull common factors out one at a time, instead of factoring the GCF in one step.

## Error Troubleshooting

In *Review Questions* 9 and 12-16, remind students to set the monomial factor

- Caution students against dividing by variables. In doing so, they will lose as a solution. See also Example 6.

General Tip: Check that students are using the zero-product property correctly.

Examples:

a. *Solve for*

(Are students incorrectly setting each factor equal to

b. *Solve for*

(Are students incorrectly setting each factor equal to ?)

General Tip: Remind students when factoring the GCF out of itself to leave a

For example, *Review Questions* 3 and 15.

General Tip: Have students check their work by expanding the factored polynomial.

- By checking a problem worked out as
6ax2−9ax+3a=3a(2x2−3x) , students will convince themselves that a1 is missing.

General Tip: Suggest that students look carefully over the remaining terms after having factored out the GCF so as to not leave any other common factors.

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