Question

Question 11
If $x^{51}+51$ is divided by x + 1, then the remainder is

A) 0
B) 1
C) 49
D) 50

Answer 1

The answer is D.
Let $p\left(x\right)=x^{51}+51$ ...(i)
When, we divide p(x) by x+1, we get the remainder equal to p(-1).
On putting x=-1 in eq.(i), we get,
$p(-1)=-1^{51}+51=-1+51=50$
Hence, the remainder is 50.