Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises - Page 44: 45



Work Step by Step

When factoring $ax^{2}+bx+c$, we search for factors of $ac$ whose sum is $b,$ and, if we find them, we rewrite $bx$ and proceed to factor in groups. Here, factors of $(5)\times(-6)=-30$ that add to $-7$ are ....$+3$ and $-10.$ $5a^{2}-7ab-6b^{2}=5a^{2}+3ab-10ab-6b^{2}$ $=\left(5a^{2}+3ab\right)+\left(-10ab-6b^{2}\right)$ $=a(5a+3b)-2b(5a+3b)$ $=(5a+3b)(a-2b)$
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