If x^{51} + 51 is divided by x + 1,the remain | vedclass

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Question

(D) According to the Remainder Theorem,if a polynomial $p(x)$ is divided by $x + a$,the remainder is $p(-a)$.Here,$p(x) = x^{51} + 51$ is divided by $

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(D) According to the Remainder Theorem,if a polynomial $p(x)$ is divided by $x + a$,the remainder is $p(-a)$.Here,$p(x) = x^{51} + 51$ is divided by $x + 1$.Therefore,the remainder is $p(-1) = (-1)^{51} + 51$.Since $(-1)$ raised to an odd power is $-1$,we have $p(-1) = -1 + 51 = 50$.Hence,the correct option is $D$.

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

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