Question

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

• A. 0
• B. 1
• C. 49
• D. 50

Answer 1

The correct option is D

50

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

When we divide $p\left(x\right)$ by $x+1$, we get the remainder $p(-1)$

On putting $x=-1$ in Eq. (i), we get $p(-1)=(-1)51+51$

= $-1+51=50$

Hence, the remainder is $50$.