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: 43

Answer

$3(x+2)(x+3)$

Work Step by Step

Factoring the $GCF= 3 ,$ the given expression, $ 3x^2+15x+18 ,$ is equivalent to \begin{array}{l}\require{cancel} 3(x^2+5x+6) .\end{array} The trinomial expression above has $c= 6 $ and $b= 5 .$ 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(x+2)(x+3) .\end{array}
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