Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - Mid-Chapter Review - Mixed Review: 19

Answer

$(1+x)(5-2x)$

Work Step by Step

Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} 5+3x-2x^2 \end{array} has $ac= 5(-2)=-10 $ and $b= 3 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ 5,-2 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} 5+5x-2x-2x^2 .\end{array} Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (5+5x)-(2x+2x^2) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 5(1+x)-2x(1+x) .\end{array} Factoring the $GCF= (1+x) $ of the entire expression above results to \begin{array}{l}\require{cancel} (1+x)(5-2x) .\end{array}
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