Intermediate Algebra (6th Edition)

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

Chapter 5 - Section 5.7 - Factoring by Special Products - Exercise Set: 2

Answer

$(x-5)^2$

Work Step by Step

The two numbers whose product is $ac= 1(25)=25 $ and whose sum is $b= -10 $ are $\{ -5,-5 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ x^2-10x+25 $, is \begin{array}{l}\require{cancel} x^2-5x-5x+25 \\\\= (x^2-5x)-(5x-25) \\\\= x(x-5)-5(x-5) \\\\= (x-5)(x-5) \\\\= (x-5)^2 .\end{array}
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