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 R - Elementary Algebra Review - R.5 Polynomials and Factoring - R.5 Exercise Set: 15

Answer

$(4x+5)(2x+3)$

Work Step by Step

Using factoring of trinomials in the form $ax^2+bx+c,$ the given expression, $ 8x^2+22x+15 ,$ has $ac$ equal to $ 8(15)=120 $ and $b$ equal to $ 22 .$ The $2$ numbers that have a product of $ac$ and a sum of $b$ are $\left\{ 10,12 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} 8x^2+10x+12x+15 .\end{array} Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to \begin{array}{l}\require{cancel} (8x^2+10x)+(12x+15) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 2x(4x+5)+3(4x+5) .\end{array} Factoring the $GCF= (4x+5) $ of the entire expression above results to \begin{array}{l}\require{cancel} (4x+5)(2x+3) .\end{array}
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