Find the remainder when x^{3}+3x^{2}+3x+1 is | vedclass

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(A) Let $p(x) = x^{3}+3x^{2}+3x+1$.According to the Remainder Theorem,when a polynomial $p(x)$ is divided by $(x-a)$,the remainder is $p(a)$.Here,the

Vedclass · Accepted Answer

$-\pi^{3}+3\pi^{2}-3\pi+1$

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(A) Let $p(x) = x^{3}+3x^{2}+3x+1$.According to the Remainder Theorem,when a polynomial $p(x)$ is divided by $(x-a)$,the remainder is $p(a)$.Here,the divisor is $x+\pi$,which can be written as $x-(-\pi)$.So,we need to find $p(-\pi)$.Substituting $x = -\pi$ in $p(x)$:$p(-\pi) = (-\pi)^{3} + 3(-\pi)^{2} + 3(-\pi) + 1$$p(-\pi) = -\pi^{3} + 3\pi^{2} - 3\pi + 1$Thus,the required remainder is $-\pi^{3}+3\pi^{2}-3\pi+1$.

Find the remainder when $x^{3}+3x^{2}+3x+1$ is divided by $x+\pi$.

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