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: 50

Answer

$(x-3)(5x+1)$

Work Step by Step

The two numbers whose product is $ac= 5(-3)=-15 $ and whose sum is $b= -14 $ are $\{ -15,1 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 5x^2-14x-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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