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: 91



Work Step by Step

Factor out $-1$ to obtain: $15+2x-x^2 \\=-1(-15-2x+x^2) \\=-1(x^2-2x-15)$ 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 $b=-2$ and $c=-15$. Note that $-15=-5(3)$ and $-2= (-5)+3$. This means that $d=-5$ and $e=3$ Thus, the factored form of the trinomial is: $(x-5)(x+3)$ Therefore, the completely factored form of the given expression is: $-1(x-5)(x+3)$
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