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 - 5.3 Factoring Trinomials of the Type ax2+bx+c - 5.3 Exercise Set - Page 326: 22



Work Step by Step

Factoring the $GCF= 2 ,$ the given expression is equivalent to \begin{array}{l}\require{cancel} 28x^2+38x-6 \\\\= 2(14x^2+19x-3) .\end{array} Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} 2(14x^2+19x-3) \end{array} has $ac= 14(-3)=-42 $ and $b= 21,-2 .$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} 2(14x^2+21x-2x-3) .\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} 2[(14x^2+21x)-(2x+3)] .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 2[7x(2x+3)-(2x+3)] .\end{array} Factoring the $GCF= (t+2) $ of the entire expression above results to \begin{array}{l}\require{cancel} 2[(2x+3)(7x-1)] \\\\= 2(2x+3)(7x-1) .\end{array}
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