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: 58



Work Step by Step

The two numbers whose product is $ac= 24(-21)=-504 $ and whose sum is $b= -47 $ are $\{ -56,9 \}$. Using these two numbers to decompose the middle term of the expression, $ 24x^2-47x-21 ,$ then the factored form is \begin{array}{l} 24x^2-56x+9x-21 \\\\= (24x^2-56x)+(9x-21) \\\\= 8x(3x-7)+3(3x-7) \\\\= (3x-7)(8x+3) .\end{array}
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