Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set: 55

Answer

$2r(r-4)(r+8)$

Work Step by Step

Factoring the $GCF= 2r ,$ the given expression, $ 2r^3+8r^2-64r ,$ is equivalent to \begin{array}{l}\require{cancel} 2r(r^2+4r-32) .\end{array} The trinomial expression above has $c= -32 $ and $b= 4 .$ The possible factors of $c$ are $ \{ 1,-32 \} ,\{ 2,-16 \} ,\{ 4,-8 \} \{ -1,32 \} ,\{ -2,16 \} ,\{ -4,8 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -4,8 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} 2r(r-4)(r+8) .\end{array}
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