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: 5

Answer

$(x+7)(2x-1)$

Work Step by Step

Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} 2x^2+13x-7 \end{array} has $ac= 2(-7)=-14 $ and $b= 13 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ 14,-1 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} 2x^2+14x-1x-7 .\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} (2x^2+14x)-(x+7) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 2x(x+7)-(x+7) .\end{array} Factoring the $GCF= (x+7) $ of the entire expression above results to \begin{array}{l}\require{cancel} (x+7)(2x-1) .\end{array}
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