What is the remainder when $x^{51}+51$ is divided by $x+1$?
$\mathrm{(A)\ } 0 \qquad \mathrm{(B) \ }1 \qquad \mathrm{(C) \  } 49 \qquad \mathrm{(D) \  } 50 \qquad \mathrm{(E) \  }51$
From the [Remainder Theorem](https://artofproblemsolving.com/wiki/index.php/Remainder_Theorem), the remainder when $x^{51}+51$ is divided by $x+1$ is $(-1)^{51}+51=-1+51=50, \boxed{\text{D}}$.