The remainder obtained on dividing x^{3}+2x^{ | vedclass

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(A) To find the remainder when the polynomial $p(x) = x^{3}+2x^{2}+3x+5$ is divided by $x+1$,we use the Remainder Theorem.According to the Remainder T

Vedclass · Accepted Answer

$3$

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(A) To find the remainder when the polynomial $p(x) = x^{3}+2x^{2}+3x+5$ is divided by $x+1$,we use the Remainder Theorem.According to the Remainder Theorem,if 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,$a = -1$.Now,we calculate $p(-1)$:$p(-1) = (-1)^{3} + 2(-1)^{2} + 3(-1) + 5$$p(-1) = -1 + 2(1) - 3 + 5$$p(-1) = -1 + 2 - 3 + 5$$p(-1) = 3$Therefore,the remainder is $3$.

The remainder obtained on dividing $x^{3}+2x^{2}+3x+5$ by $x+1$ is ..............

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