<meta http-equiv="refresh" content="1; url=/nojavascript/"> Polynomial Equations in Factored Form | CK-12 Foundation
You are reading an older version of this FlexBook® textbook: CK-12 Algebra I Teacher's Edition Go to the latest version.

# 9.4: Polynomial Equations in Factored Form

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 $(a + b)(x + y) \Rightarrow ax + bx + ay + by$; they will now learn to “put it back together”: $ax + bx + ay + by \Rightarrow (a + b)(x + y)$.
• 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 $(x, y, a,$ or $b)$ equal to zero.

• Caution students against dividing by variables. In doing so, they will lose $0$ as a solution. See also Example 6.

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

Examples:

a. Solve for $x$.

$(x + 3)(x - 4) = 8$

(Are students incorrectly setting each factor equal to $8$?)

b. Solve for $x$.

$(x + 3)(x - 4) - 2 = 0$

(Are students incorrectly setting each factor equal to $0$?)

General Tip: Remind students when factoring the GCF out of itself to leave a $1$.

For example, $6ax^2 - 9ax + 3a \neq 3a(2x^2 - 3x)$; but $6ax^2 - 9ax + 3a = 3a(2x^2 - 3x + 1)$. 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 $6ax^2 - 9ax + 3a = 3a(2x^2 - 3x)$, students will convince themselves that a $1$ 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.

Feb 22, 2012

Aug 22, 2014

# Reviews

Image Detail
Sizes: Medium | Original

CK.MAT.ENG.TE.1.Algebra-I.9.4