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: 34

Answer

$(x+3)(3x+5)$

Work Step by Step

The two numbers whose product is $ac= 3(15)=45 $ and whose sum is $b= 14 $ are $\{ 5,9 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 3x^2+14x+15 $, is \begin{array}{l}\require{cancel} 3x^2+9x+5x+15 \\\\= (3x^2+9x)+(5x+15) \\\\= 3x(x+3)+5(x+3) \\\\= (x+3)(3x+5) .\end{array}
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