Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set: 47

Answer

$8mn(m-3n)(m-1)$

Work Step by Step

Factoring the $GCF= 8mn $, then the given expression, $ 8m^3n-32m^2n^2+24mn $ is equivalent to \begin{array}{l} 8mn(m^2-4mn+3) .\end{array} The two numbers whose product is $ac= 1(3)=3 $ and whose sum is $b= -4 $ are $\{ -3,-1 \}$. Using these two numbers to decompose the middle term of the expression, $ 8mn(m^2-4mn+3) ,$ then the factored form is \begin{array}{l} 8mn(m^2-3mn-1mn+3) \\\\= 8mn[(m^2-3mn)-(1mn-3)] \\\\= 8mn[m(m-3n)-(mn-3)] \\\\= 8mn[(m-3n)(m-1)] \\\\= 8mn(m-3n)(m-1) .\end{array}
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