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 303: 15



Work Step by Step

The two numbers whose product is $ac= 5(3)=15 $ and whose sum is $b= 16 $ are $\{ 1,15 \}$. Using these two numbers to decompose the middle term, then the factored form of the given expression, $ 5x^2+16x+3 $,is \begin{array}{l}\require{cancel} 5x^2+15x+x+3 \\\\= (5x^2+15x)+(x+3) \\\\= 5x(x+3)+(x+3) \\\\= (x+3)(5x+1) .\end{array}
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