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

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(B) Let $p(x) = x^{3}+3x^{2}+3x+1$.To find the remainder when $p(x)$ is divided by $5+2x$,we use the Remainder Theorem.First,find the zero of the divi

Vedclass · Accepted Answer

$-\frac{27}{8}$

Vedclass · Answer

(B) Let $p(x) = x^{3}+3x^{2}+3x+1$.To find the remainder when $p(x)$ is divided by $5+2x$,we use the Remainder Theorem.First,find the zero of the divisor $5+2x$:$5+2x = 0 \implies 2x = -5 \implies x = -\frac{5}{2}$.Now,evaluate $p(-\frac{5}{2})$:$p(-\frac{5}{2}) = (-\frac{5}{2})^{3} + 3(-\frac{5}{2})^{2} + 3(-\frac{5}{2}) + 1$$= -\frac{125}{8} + 3(\frac{25}{4}) - \frac{15}{2} + 1$$= -\frac{125}{8} + \frac{75}{4} - \frac{15}{2} + 1$$= \frac{-125 + 150 - 60 + 8}{8}$$= \frac{-27}{8}$.Thus,the required remainder is $-\frac{27}{8}$.

Find the remainder when $x^{3}+3x^{2}+3x+1$ is divided by $5+2x$.

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