# 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 .
- 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 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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### Image Attributions

## Description

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## Tags:

Activities
Answer Key
Answers
(43 more)
Assessment
binomial
binomial formula
CK.MAT.ENG.TE.1.Algebra-I.9
coefficients
Common Misconceptions
Concept Check and Troubleshooting
constant
cubic term
degree
degree of polynomials
Differentiated Instruction
distributive property
Enrichment
factoring quadratic expressions
greatest common monomial factor
Inquiry Process
leading coefficient
leading term
linear term
monomial
Pacing
perfect square trinomial
polynomials
Problem Sets
Problem Solving
quadratic term
Quizzes
Science Inquiry
simplifying polynomials
Solution Key
Solutions
square of a binomial
standard form
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
term
Testing
Tests
trinomial
Worksheets
zero-product property

## Subjects:

## Date Created:

Feb 22, 2012## Last Modified:

Aug 22, 2014
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