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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