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: 59

Answer

$(x+1)(25x+64)$

Work Step by Step

Rearranging the terms, the given expression is equivalent to \begin{array}{l}\require{cancel} 89x+64+25x^2 \\\\= 25x^2+89x+64 .\end{array} Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} 25x^2+89x+64 \end{array} has $ac= 25(64)=1600 $ and $b= 89 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ 25,64 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} 25x^2+25x+64x+64 .\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} (25x^2+25x)+(64x+64) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 25x(x+1)+64(x+1) .\end{array} Factoring the $GCF= (x+1) $ of the entire expression above results to \begin{array}{l}\require{cancel} (x+1)(25x+64) .\end{array}
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