Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Section 5.2 - Factoring Trinomials - 5.2 Exercises: 49

Answer

$-11x(x-4)(x-6)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ First, factor the GCF of the terms. Then, to factor the quadratic expression $x^2+bx+c,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$. Express the factored form as $GCF(x+m_1)(x+m_2).$ $\bf{\text{Solution Details:}}$ Using the negative $GCF= -11x ,$ the given expression, $ -11x^3+110x^2-264x ,$ is equivalent to \begin{array}{l}\require{cancel} -11x(x^2-10x+24) .\end{array} In the expression above, the value of $c$ is $ 24 $ and the value of $b$ is $ -10 .$ The possible pairs of integers whose product is $ac$ are \begin{array}{l}\require{cancel} \{1,24\}, \{2,12\}, \{3,8\}, \{4,6\}, \{-1,-24\}, \{-2,-12\}, \{-3,-8\}, \{-4,-6\} .\end{array} Among these pairs, the one that gives a sum of $b$ is $\{ -4,-6 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} -11x(x-4)(x-6) .\end{array}
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