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: 54

Answer

$3m^2(m-4)(m+6)$

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 $GCF(x+m_1)(x+m_2).$ $\bf{\text{Solution Details:}}$ Factoring the $GCF= 3m^2 ,$ the given expression, $ 3m^4+6m^3-72m^2 ,$ is equivalent to \begin{array}{l}\require{cancel} 3m^2(m^2+2m-24) .\end{array} In the expression above, the value of $c$ is $ -24 $ and the value of $b$ is $ 2 .$ 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} 3m^2(m-4)(m+6) .\end{array}
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