Intermediate Algebra (6th Edition)

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

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 48

Answer

$2(2x-1)(2x-1)$ or $2(2x-1)^{2}$

Work Step by Step

$8x^{2}-8x+2$ Factor out greatest common factor $2$ $=2(4x^{2}-4x+1)$ In this trinomial $(4x^{2}-4x+1)$, $a=4$, $b=-4$ and $c=1$. Splitting the middle term $b$ into two numbers whose product is $4$ $(a \times c)$ and whose sum is $(b)$ $-4$. The numbers are $-2$ and $-2$. $=2(4x^{2}-2x-2x+1)$ Factor out by grouping. $=2((4x^{2}-2x)+(-2x+1))$ $=2(2x(2x-1)-1(2x-1))$ $=2((2x-1)(2x-1))$ $=2(2x-1)(2x-1)$ $=2(2x-1)^{2}$
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