The remainder obtained when the polynomial x^ | vedclass

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Question

(A) According to the Remainder Theorem,when a polynomial $p(x)$ is divided by $(x - a)$,the remainder is $p(a)$.Here,the divisor is $(x + 1)$,which ca

Vedclass · Accepted Answer

$1$

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(A) According to the Remainder Theorem,when a polynomial $p(x)$ is divided by $(x - a)$,the remainder is $p(a)$.Here,the divisor is $(x + 1)$,which can be written as $(x - (-1))$.Therefore,we need to evaluate $p(-1)$ for the polynomial $p(x) = x^{64} + x^{27} + 1$.$p(-1) = (-1)^{64} + (-1)^{27} + 1$.Since $64$ is an even number,$(-1)^{64} = 1$.Since $27$ is an odd number,$(-1)^{27} = -1$.Thus,$p(-1) = 1 + (-1) + 1 = 1 - 1 + 1 = 1$.The remainder is $1$.

The remainder obtained when the polynomial $x^{64} + x^{27} + 1$ is divided by $(x + 1)$ is:

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