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: 92

Answer

The polynomial is prime.

Work Step by Step

Factor out $-1$ to obtain: $14+6x-x^2 \\=-1(-14-6x+x^2) \\=-1(x^2-6x-14)$ 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 $b=-6$ and $c=-14$. Note that $-14$ has no factors whose sum is $-6$. Thus, the given expression is prime.
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