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: 22

Answer

$(5x-3)^2$

Work Step by Step

The two numbers whose product is $ac= 25(9)=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 given expression, $ 25x^2-30x+9 $,is \begin{array}{l}\require{cancel} 25x^2-15x-15x+9 \\\\= (25x^2-15x)-(15x-9) \\\\= 5x(5x-3)-3(5x-3) \\\\= (5x-3)(5x-3) \\\\= (5x-3)^2 .\end{array}
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