# If $\left(x^{51}+51\right)$ is divided by

Question.

If $\left(x^{51}+51\right)$ is divided by $(x+1)$ then the remainder is

(a) 0

(b) 1

(c) 49

(d) 50

Solution:

Let $f(x)=x^{51}+51$

By remainder theorem, when f(x) is divided by (x + 1), then the remainder = f(−1).

Putting x = −1 in f(x), we get

$f(-1)=(-1)^{51}+51=-1+51=50$

∴ Remainder = 50

Thus, the remainder when $\left(x^{51}+51\right)$ is divided by $(x+1)$ is 50

Hence, the correct answer is option (d).