Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-8 Factoring by Grouping - Practice and Problem-Solving Exercises - Page 532: 39


Sample answer: $2x^{3}+x^{2}+6x+3=(2x+1)(x^{2}+3)$

Work Step by Step

Working backwards, select a binomial that will be a common factor, say $2x+1.$ For the first group, multiply it with $x^{2},$ $x^{2}(2x+1)=2x^{3}+x^{2}$ for the second group, multiply it with 3, $3(2x+1)=6x+3$ So, our four term polynomial is $2x^{3}+x^{2}+6x+3$ $2x^{3}+x^{3}+6x+3=x^{2}(2x+1)+3(2x+1)$ $=(2x+1)(x^{2}+3)$
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