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: 16

Answer

$4(x-5)^2$

Work Step by Step

Factoring the $GCF=4,$ the given expression is equivalent to \begin{array}{l}\require{cancel} 4x^2-40x+100 \\\\= 4(x^2-10x+25) .\end{array} Using the factoring of trinomials in the form $x^2+bx+c,$ the expression above has $c$ equal to $ 25 $ and $b$ equal to $ -10 .$ The two numbers that give a product of $c$ and a sum of $b$ are $\{ -5,-5 \}.$ Hence, the factored form of the expression above is \begin{array}{l}\require{cancel} 4(x-5)(x-5) \\\\= 4(x-5)^2 .\end{array}
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