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 - Page 344: 17



Work Step by Step

Factoring the $GCF= 3x $, then the given expression, $ 9x^3+12x^2-45x $ is equivalent to \begin{array}{l} 3x(3x^2+4x-15) .\end{array} The two numbers whose product is $ac= 3(-15)=-45 $ and whose sum is $b= 4 $ are $\{ 9,-5 \}$. Using these two numbers to decompose the middle term of the trinomial above, then the complete factored form is \begin{array}{l} 3x(3x^2+4x-15) \\\\= 3x(3x^2+9x-5x-15) \\\\= 3x[(3x^2+9x)-(5x+15)] \\\\= 3x[3x(x+3)-5(x+3)] \\\\= 3x[(x+3)(3x-5)] \\\\= 3x(x+3)(3x-5) .\end{array}
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