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: 30

Answer

$(5x-11)(7x+4)$

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^2-57x-44 \end{array} has $ac= 35(-44)=1540 $ and $b= -57 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ -77,20 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} 35x^2-77x+20x-44 .\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^2-77x)+(20x-44) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 7x(5x-11)+4(5x-11) .\end{array} Factoring the $GCF= (5x-11) $ of the entire expression above results to \begin{array}{l}\require{cancel} (5x-11)(7x+4) .\end{array}
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