Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - Chapter Review - Page 270: 29



Work Step by Step

Factoring the negative $GCF= -2 ,$ the given $\text{ expression ,} -4x^2+14x-6 ,$ is equivalent to \begin{align*} -2(2x^2-7x+3) .\end{align*} Using the factoring of trinomials in the form $ax^2+bx+c,$ the expression \begin{align*} -2(2x^2-7x+3) \end{align*} has $ac= 2(3)=6 $ and $b= -7 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ -1,-6 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{align*} -2(2x^2-x-6x+3) .\end{align*} Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to \begin{align*} -2[(2x^2-x)-(6x-3)] .\end{align*} Factoring the $GCF$ in each group results to \begin{align*} -2[x(2x-1)-3(2x-1)] .\end{align*} Factoring the $GCF= (2x-1) $ of the entire expression above results to \begin{align*} & -2[(2x-1)(x-3)] \\&= -2(2x-1)(x-3) .\end{align*}
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