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,th

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(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 $x + 1$,which can be written as $x - (-1)$. Thus,$a = -1$.To find the remainder,we calculate $p(-1)$:$p(-1) = (-1)^{3} + 3(-1)^{2} + 3(-1) + 1$$p(-1) = -1 + 3(1) - 3 + 1$$p(-1) = -1 + 3 - 3 + 1$$p(-1) = 0$.Therefore,the required remainder is $0$.

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

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