Question

If $x^{51}+51$ is divided by $x+1$, the remainder is

Answer 1

Given: $x^{51}+51$

Let, $f\left(x\right)=x^{51}+51$

$\because f\left(x\right)$ is divided by $x+1$, so by factor theorem remainder $=f(-1)$.

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

$=-1+51=50$

$\because$ The remainder is $50$.

Hence, option (D) is the correct answer.