Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 5 - Section 5.4 - Factoring Trinomials - Exercise Set - Page 362: 89

Answer

$(x+2)(5x+12)$.

Work Step by Step

The given expression is $=5(x+1)^{2}+12(x+1)+7$ Substitute $x+1=u$. $=5(u)^2+12u+7$ Simplify. $=5u^2+12u+7$ Rewrite $12u$ as $5u+7u$. $=5u^2+5u+7u+7$ Factor. $=5u(u+1)+7(u+1)$ $=(u+1)(5u+7)$. Substitute back $u=x+1$. $=((x+1)+1)(5(x+1)+7)$. Simplify. $=(x+1+1)(5x+5+7)$. $=(x+2)(5x+12)$.
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