$29 \cdot 57$ When $x^{51}+51$ is divided by $x+1$, the remainder is
(A) 0 .
(B) 1 .
(C) 49 .
(D) 50 .
(E) 51 .
(25th American High School Mathematics Examination, 1974)
[Solution] By the Remainder Theorem, the remainder of $f(x)=x^{51}+51$ divided by $x+1$ is
$$
f(-1)=(-1)^{51}+51=50 \text {. }
$$

Therefore, the correct choice is $(D)$.