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: 36



Work Step by Step

Factoring the $GCF= 5 ,$ the given expression is equivalent to \begin{array}{l}\require{cancel} 20y^2-25y+5 \\\\= 5(4y^2-5y+1) .\end{array} Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} 5(4y^2-5y+1) \end{array} has $ac= 4(1)=4 $ and $b= -5 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ -4,-1 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} 5(4y^2-4y-1y+1) .\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} 5[(4y^2-4y)-(y-1)] .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 5[4y(y-1)-(y-1)] .\end{array} Factoring the $GCF= (y-1) $ of the entire expression above results to \begin{array}{l}\require{cancel} 5[(y-1)(4y-1)] \\\\= 5(y-1)(4y-1) .\end{array}
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