The remainder obtained when the polynomial x^ | vedclass

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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,$P(x) = x^{64} + x^{27} + 1$ and

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$1$

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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,$P(x) = x^{64} + x^{27} + 1$ and the divisor is $(x + 1)$,which is $(x - (-1))$.Therefore,the remainder is $P(-1) = (-1)^{64} + (-1)^{27} + 1$.Since $64$ is an even number,$(-1)^{64} = 1$.Since $27$ is an odd number,$(-1)^{27} = -1$.Thus,the remainder is $1 + (-1) + 1 = 1 - 1 + 1 = 1$.

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

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