2. Polynomials
easy

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

A

$0$

B

$1$

C

$49$

D

$50$

Solution

If $p ( x )$ is divided by $x + a$, then the remainder is $p (- a )$.

Here $p(x)=x^{51}+51$ is divided by $x +1,$ then

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

Hence, $(d)$ is the correct answer.

Standard 9
Mathematics

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