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: 47



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 $(12)\times(-1)=-12$ that add to $-1$ are ....$+3$ and $-4.$ $12x^{2}-xy-y^{2}=12x^{2}+3xy-4xy-y^{2}$ $=\left(12x^{2}+3xy\right)+\left(-4xy-y^{2}\right)$ $=3x(4x+y)-y(4x+y)$ $=(4x+y)(3x-y)$
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