Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Review Exercises: 7

Answer

$(n+4)(m+q)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $ 4m+nq+mn+4q ,$ 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 third terms and the second and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (4m+mn)+(nq+4q) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} m(4+n)+q(n+4) \\\\= m(n+4)+q(n+4) .\end{array} Factoring the $GCF= (n+4) $ of the entire expression above results to \begin{array}{l}\require{cancel} (n+4)(m+q) .\end{array}
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