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: 45

Answer

$(x+5y)(3x-2y)$

Work Step by Step

The two numbers whose product is $ac= 3(-10)=-30 $ and whose sum is $b= 13 $ are $\{ 15,-2 \}$. Using these two numbers to decompose the middle term of the given expression, $ 3x^2+13xy-10y^2 ,$ then the factored form is \begin{array}{l} 3x^2+15xy-2xy-10y^2 \\\\= (3x^2+15xy)-(2xy+10y^2) \\\\= 3x(x+5y)-2y(x+5y) \\\\= (x+5y)(3x-2y) .\end{array}
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