Answer
$(x+1)^{2}(x^{2}-x+1)$
Work Step by Step
We factor by grouping to obtain:
$x^{4}+x^{3}+x+1=x^{3}(x+1)+1(x+1)
=(x^{3}+1)(x+1)
=(x+1)(x+1)(x^{2}-x+1)
=(x+1)^{2}(x^{2}-x+1)$
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: 126
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