Problem: When x9−x is factored as completely as possible into polynomials and monomials with integral coefficients, the number of factors is:
Answer Choices:
A. more than 5
B. 5
C. 4
D. 3
E. 2
Solution:
x9−x=x(x8−1)=x(x4+1)(x4−1)
=x(x4+1)(x2+1)(x+1)(x−1)