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 221: 44

Answer

$(3x-5)(x+4)$

Work Step by Step

Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression, \begin{align*} 3x^2+7x-20 \end{align*} has $ac= 3(-20)=-60 $ and $b= 7 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ -5,12 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{align*} 3x^2-5x+12x-20 \end{align*} Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to \begin{align*} (3x^2-5x)+(12x-20) \end{align*} Factoring the $GCF$ in each group results to \begin{align*} x(3x-5)+4(3x-5) \end{align*} Factoring the $GCF= (3x-5) $ of the entire expression above results to \begin{align*} (3x-5)(x+4) \end{align*}
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