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: 42



Work Step by Step

Factor out the greatest common factor, $2x$ $=2x\left(18x^{2}+9x-2\right)$ 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 $(18)\times(-2)=-36$ that add to $+9$ are ....$+12$ and $-3.$ $=2x\left(18x^{2}-3x+12x-2\right)$ $=2x\left[ \left(18x^{2}-3x\right)+(12x-2) \right]$ $=2x\left[ 3x(6x-1)+2(6x-1) \right]$ $=2x(6x-1)(3x+2)$
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