Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 76

Answer

$x(y-1)(5y-4)$

Work Step by Step

Factoring the $GCF=x$, then the given expression, $ 5xy^2-9xy+4x $, is equivalent to \begin{array}{l} x(5y^2-9y+4) .\end{array} The two numbers whose product is $ac= 5(4)=20 $ and whose sum is $b= -9 $ are $\{ -5,-4 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ x(5y^2-9y+4) $, is \begin{array}{l}\require{cancel} x(5y^2-5y-4y+4) \\\\= x[(5y^2-5y)-(4y-4)] \\\\= x[5y(y-1)-4(y-1)] \\\\= x[(y-1)(5y-4)] \\\\= x(y-1)(5y-4) .\end{array}
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