## Introductory Algebra for College Students (7th Edition)

Published by Pearson

# Chapter 6 - Section 6.1 - The Greatest Common Factor and Factoring by Grouping - Exercise Set - Page 428: 105

#### Answer

Steps: 1. Group terms that have a common monomial factor. 2. Factor out the common monomial factor from each group. 3. Factor out the remaining common binomial factor . (see example in step-by-step)

#### Work Step by Step

Factoring by Grouping: 1. Group terms that have a common monomial factor. There will usually be two groups. Sometimes the terms must be rearranged. 2. Factor out the common monomial factor from each group. 3. Factor out the remaining common binomial factor (if one exists). Example: $2x^{3}-4x^{2}+8x-16$ 1. Group terms that have a common monomial factor. There will usually be two groups. Sometimes the terms must be rearranged. $2x^{3}-4x^{2}+7x-14=[2x^{3}-4x^{2}]+[7x-14]$ 2. Factor out the common monomial factor from each group. $...=2x^{2}(x-2)+7(x-2)$ 3. Factor out the remaining common binomial factor $...=(x-2)(2x^{2}+7)$

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