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: 46

Answer

$3(y-2)(y+3)$

Work Step by Step

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