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: 57

Answer

$(x-4)(x+3)$

Work Step by Step

The two numbers whose product is $ac= 1(-12)=-12 $ and whose sum is $b= -1 $ are $\{ -4,3 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ x^2-x-12 $, is \begin{array}{l}\require{cancel} x^2-4x+3x-12 \\\\= (x^2-4x)+(3x-12) \\\\= x(x-4)+3(x-4) \\\\= (x-4)(x+3) .\end{array}
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