Question

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

• A. 0
• B. 1
• C. 49
• D. 50

Answer 1

The correct option is D 50

The zero of $x+1$ is -1 and $p\left(x\right)=x^{51}+51$.
So, $p(-1)=(-1{)}^{51}+51=-1+51=50$.
Therefore, by Remainder theorem, when $p\left(x\right)=x^{51}+51$ is divided by $x+1$ the remainder is 50.
Option D is correct.