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: 63

Answer

$15x(x-1)(x+4)$

Work Step by Step

Factoring the $GCF= 15x ,$ the given expression, $ 15xy^2+45xy-60x ,$ is equivalent to \begin{array}{l}\require{cancel} 15x(y^2+3y-4) .\end{array} The trinomial expression above has $c= -4 $ and $b= 3 .$ The possible factors of $c$ are $ \{ 1,-4 \} ,\{ 2,-2 \} ,\{ -1,4 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -1,4 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} 15x(x-1)(x+4) .\end{array}
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