Algebra 2 Common Core

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

Chapter 4 - Quadratic Functions and Equations - 4-4 Factoring Quadratic Expressions - Practice and Problem-Solving Exercises - Page 222: 79



Work Step by Step

Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression, $ 4x^2+15x-4 ,$ $ac= 4(-4)=-16 $ and $b= 15 .$ The two numbers with a product of $ac$ and a sum of $b$ are $\left\{ -1,16 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{align*} 4x^2-x+16x-4 .\end{align*} Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to \begin{align*} (4x^2-x)+(16x-4) .\end{align*} Factoring the $GCF$ in each group results to \begin{align*} x(4x-1)+4(4x-1) .\end{align*} Factoring the $GCF= (4x-1) $ of the entire expression above results to \begin{align*} (4x-1)(x+4) .\end{align*} Hence, the answer is Choice D.
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