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: 21

Answer

$-(5x+2)(7x+4)$

Work Step by Step

Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} -35x^2-34x-8 \end{array} has $ac= -35(-8)=280 $ and $b= -14,-20 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ 15,16 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} -35x^2-14x-20x-8 .\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} (-35x^2-14x)-(20x+8) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} -7x(5x+2)-4(5x+2) .\end{array} Factoring the $GCF= (5x+2) $ of the entire expression above results to \begin{array}{l}\require{cancel} (5x+2)(-7x-4) \\\\= -(5x+2)(7x+4) .\end{array}
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