Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Sections 5.1-5.7 - Integrated Review - Operations on Polynomials and Factoring Strategies: 12

Answer

$2x(2x-1)$

Work Step by Step

The two numbers whose product is $ac= 1(2)=2 $ and whose sum is $b= -3 $ are $\{ -1,-2 \}$. Using these two numbers to decompose the middle term of the given expression, $ (2x+1)^2-3(2x+1)+2 $, results to \begin{array}{l} (2x+1)^2-2(2x+1)-1(2x+1)+2 \\\\= [(2x+1)^2-2(2x+1)]-[1(2x+1)-2] \\\\= (2x+1)[(2x+1)-2]-[(2x+1)-2] \\\\= [(2x+1)-2][(2x+1)-1] \\\\= (2x+1-2)(2x+1-1) \\\\= (2x-1)(2x) \\\\= 2x(2x-1) .\end{array}
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