Answer
$x^{2}+x+1$ is prime. Check proof below.
Work Step by Step
First we list the pairs of integers whose product is 1, along with their sum:
1 and 1 -> 2
-1 and -1 -> -2
None of these sums are equal to 1, therefore $x^{2}+x+1$ is prime
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter R - Section R.5 - Factoring Polynomials - R.5 Exercises - Page 58: 138
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