Intermediate Algebra (6th Edition)

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

Chapter 5 - Sections 5.1-5.7 - Integrated Review - Operations on Polynomials and Factoring Strategies - Page 313: 22

Answer

$(5x+4)^2$

Work Step by Step

The two numbers whose product is $ 25(16)=40 $ and whose sum is $ 40 $ are $\{ 20,20 \}$. Using these numbers to decompose the middle term of the trinomial results to \begin{array}{l} 25x^2+40x+16 \\= 25x^2+20x+20x+16 \\= (25x^2+20x)+(20x+16) \\= 5x(5x+4)+4(5x+4) \\= (5x+4)(5x+4) \\= (5x+4)^2 .\end{array}
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