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: 44



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 $(14)\times(-15)=-210$ that add to $+11$ are ....$+21$ and $-10.$ $14m^{2}+11mr-15r^{2}= 14m^{2}-10mr+21mr-15r^{2}$ $=\left(14m^{2}-10mr\right)+\left(21mr-15r^{2}\right)$ $=2m(7m-5r)+3r(7m-5r)$ $=(7m-5r)(2m+3r)$
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