College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.5 - Factoring Polynomials - R.5 Exercises: 93

Answer

$3(x-6)(x+2)$

Work Step by Step

Factor out $3$ to obtain: $=3(x^2-4x-12)$ RECALL: A trinomial of the form $x^2+bx+c$ can be factored if there are integers $d$ and $e$ such that $c=de$ and $b=d+e$. The trinomial's factored form will be: $x^2+bx+c=(x+d)(x+e)$ The trinomial above has $b=-4$ and $c=-12$. Note that $-12=-6(2)$ and $-4= (-6)+2$. This means that $d=-6$ and $e=2$ Thus, the factored form of the trinomial is: $(x-6)(x+2)$ Therefore, the completely factored form of the given expression is: $3(x-6)(x+2)$
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