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: 18

Answer

$(x-5)(3x-4)$

Work Step by Step

The two numbers whose product is $ac= 3(20)=60 $ and whose sum is $b= -19 $ are $\{ -15,-4 \}$. Using these two numbers to decompose the middle term, then the factored form of the given expression, $ 3x^2-19x+20 $,is \begin{array}{l}\require{cancel} 3x^2-15x-4x+20 \\\\= (3x^2-15x)-(4x-20) \\\\= 3x(x-5)-4(x-5) \\\\= (x-5)(3x-4) .\end{array}
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