Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.3 Factoring Trinomials of the Type ax2+bx+c - 5.3 Exercise Set: 100

Answer

$-2(a+1)^n(a+3)^2 (a+6)$

Work Step by Step

Factoring the $GCF= (a+1)^n(a+3)^2 ,$ the given expression is equivalent to \begin{array}{l}\require{cancel} 3(a+1)^{n+1}(a+3)^2-5(a+1)^n(a+3)^3 \\\\= (a+1)^n(a+3)^2 [3(a+1)-5(a+3)] \\\\= (a+1)^n(a+3)^2 [3(a)+3(1)-5(a)-5(3)] \\\\= (a+1)^n(a+3)^2 [3a+3-5a-15] \\\\= (a+1)^n(a+3)^2 [-2a-12] \\\\= (a+1)^n(a+3)^2 (-2)(a+6) \\\\= -2(a+1)^n(a+3)^2 (a+6) .\end{array}
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