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: 53

Answer

$4x(x-3)(x+6)$

Work Step by Step

Factoring the $GCF= 4x ,$ the given expression, $ 4x^3+12x^2-72x ,$ is equivalent to \begin{array}{l}\require{cancel} 4x(x^2+3x-18) .\end{array} The trinomial expression above has $c= -18 $ and $b= 3 .$ The possible factors of $c$ are $ \{ 1,-18 \} ,\{ 2,-9 \} ,\{ 3,-6 \} ,\{ -1,18 \} ,\{ -2,9 \} ,\{ -3,6 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -3,6 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} 4x(x-3)(x+6) .\end{array}
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