Problem: What is the remainder when x51+51x^{51}+51x51+51 is divided by x+1?x+1?x+1?
Answer Choices:
A. 000
B. 111
C. 494949
D. 505050
E. 515151 Solution:
By the remainder theorem x31+51x^{31}+51x31+51 divided by x+1x+1x+1 leaves a remainder of (−1)51+51=50(-1)^{51}+51=50(−1)51+51=50. This can also be seen quite easily by long division.