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: 56

Answer

$(a+5c)(7b+1)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $ 7ab+35bc+a+5c ,$ 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} (7ab+35bc)+(a+5c) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 7b(a+5c)+1(a+5c) .\end{array} Factoring the $GCF= (a+5c) $ of the entire expression above results to \begin{array}{l}\require{cancel} (a+5c)(7b+1) .\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.