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: 49

Answer

$3(x-2)(x-9)$

Work Step by Step

Factoring the $GCF= 3 ,$ the given expression, $ 3x^2-33x+54 ,$ is equivalent to \begin{array}{l}\require{cancel} 3(x^2-11x+18) .\end{array} The trinomial expression above has $c= 18 $ and $b= -11 .$ 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 $\{ -2,-9 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} 3(x-2)(x-9) .\end{array}
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