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: 58

Answer

$(2a+1)(a^2-7)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $ 2a^3+a^2-14a-7 ,$ 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} (2a^3+a^2)-(14a+7) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} a^2(2a+1)-7(2a+1) .\end{array} Factoring the $GCF= (2a+1) $ of the entire expression above results to \begin{array}{l}\require{cancel} (2a+1)(a^2-7) .\end{array}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.