## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 5 - Section 5.4 - A General Approach to Factoring - 5.4 Exercises - Page 348: 21

#### Answer

$(k-9)(q+r)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $kq-9q+kr-9r ,$ such that the factored form of the groupings will result to a factor that is common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression. $\bf{\text{Solution Details:}}$ Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (kq-9q)+(kr-9r) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} q(k-9)+r(k-9) .\end{array} Factoring the $GCF= (k-9)$ of the entire expression above results to \begin{array}{l}\require{cancel} (k-9)(q+r) .\end{array}

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