Intermediate Algebra (12th Edition)

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

Chapter 5 - Section 5.4 - A General Approach to Factoring - 5.4 Exercises - Page 348: 18

Answer

$(m-2)(n+5)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $ mn-2n+5m-10 ,$ 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} (mn-2n)+(5m-10) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} n(m-2)+5(m-2) .\end{array} Factoring the $GCF= (m-2) $ of the entire expression above results to \begin{array}{l}\require{cancel} (m-2)(n+5) .\end{array}
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