Intermediate Algebra (12th Edition)

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

Chapter 5 - Section 5.1 - Greatest Common Factors and Factoring by Grouping - 5.1 Exercises: 57

Answer

$(m+4)(m^2-6)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $ m^3+4m^2-6m-24 ,$ such that the factored form of the groupings will result to a factor 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} (m^3+4m^2)-(6m+24) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} m^2(m+4)-6(m+4) .\end{array} Factoring the $GCF= (m+4) $ of the entire expression above results to \begin{array}{l}\require{cancel} (m+4)(m^2-6) .\end{array}
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