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: 74

Answer

$(2x+3)^2$

Work Step by Step

The two numbers whose product is $ac= 4(9)=36 $ and whose sum is $b= 12 $ are $\{ 6,6 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 4x^2+12x+9 $, is \begin{array}{l}\require{cancel} 4x^2+6x+6x+9 \\\\= (4x^2+6x)+(6x+9) \\\\= 2x(2x+3)+3(2x+3) \\\\= (2x+3)(2x+3) \\\\= (2x+3)^2 .\end{array}
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