# 9.4: Polynomial Equations in Factored Form

## 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 ; they will now learn to “put it back together”: .
- 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 or equal to zero.

- 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, ; but . See Example 5b and *Review Questions* 3 and 15.

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

- By checking a problem worked out as , students will convince themselves that a 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.