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 - Page 304: 73



Work Step by Step

The two numbers whose product is $ac= 9(25)=225 $ and whose sum is $b= 30 $ are $\{ 15,15 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 9x^2+30x+25 $, is \begin{array}{l}\require{cancel} 9x^2+15x+15x+25 \\\\= (9x^2+15x)+(15x+25) \\\\= 3x(3x+5)+5(3x+5) \\\\= (3x+5)(3x+5) \\\\= (3x+5)^2 .\end{array}
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