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: 56

Answer

$(a-5b)(a+3b)$

Work Step by Step

The two numbers whose product is $ac= 1(-15)=-15 $ and whose sum is $b= -2 $ are $\{ -5,3 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ a^2-2ab-15b^2 $, is \begin{array}{l}\require{cancel} a^2-5ab+3ab-15b^2 \\\\= (a^2-5ab)+(3ab-15b^2) \\\\= a(a-5b)+3b(a-5b) \\\\= (a-5b)(a+3b) .\end{array}
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