Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 29

Answer

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

Work Step by Step

The two numbers whose product is $ac= 2(-3)=-6 $ and whose sum is $b= -5 $ are $\{ -6,1 \}$. Using these two numbers to decompose the middle term, then the factored form of the given expression, $ 2x^2-5xy-3y^2 $,is \begin{array}{l}\require{cancel} 2x^2-6xy+xy-3y^2 \\\\= (2x^2-6xy)+(xy-3y^2) \\\\= 2x(x-3y)+y(x-3y) \\\\= (x-3y)(2x+y) .\end{array}
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