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 - Page 309: 5



Work Step by Step

The two numbers whose product is $ac= 25(1)=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, $ 25x^2+10x+1 $, is \begin{array}{l}\require{cancel} 25x^2+5x+5x+1 \\\\= (25x^2+5x)+(5x+1) \\\\= 5x(5x+1)+(5x+1) \\\\= (5x+1)(5x+1) \\\\= (5x+1)^2 .\end{array}
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