## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 5 - Section 5.1 - Greatest Common Factors and Factoring by Grouping - 5.1 Exercises: 51

#### Answer

$(2-q)(2-3p)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Factor by grouping the first $2$ and the last $2$ terms of the given expression, $4-2q-6p+3pq .$ Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression. $\bf{\text{Solution Details:}}$ Grouping the first $2$ and the last $2$ terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (4-2q)-(6p-3pq) .\end{array} Factoring the $GCF$ in each group, results to \begin{array}{l}\require{cancel} 2(2-q)-3p(2-q) .\end{array} Factoring the $GCF= (2-q)$ of the entire expression above results to \begin{array}{l}\require{cancel} (2-q)(2-3p) .\end{array}

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