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: 41



Work Step by Step

Factor out the greatest common factor, $2a$ $=2a\left(6a^{2}+5a-21\right)$ 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 $(6)\times(-21)=-126$ that add to $+5$ are ....$+9$ and $-14.$ $=2a\left(6a^{2}+9a-14a-21\right)$ $=2a\left[ \left(6a^{2}-9a\right)+(14a-21) \right]$ $=2a\left[ 3a(2a-3)+7(2a-3) \right]$ $=2a(2a-3)(3a+7)$
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