Check whether p(x) is a multiple of g(x) or n | vedclass

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(B) polynomial $p(x)$ is a multiple of $g(x)$ if and only if $g(x)$ divides $p(x)$ completely,which means the remainder must be $0$.To find the remain

Vedclass · Accepted Answer

No,it is not a multiple.

Vedclass · Answer

(B) polynomial $p(x)$ is a multiple of $g(x)$ if and only if $g(x)$ divides $p(x)$ completely,which means the remainder must be $0$.To find the remainder when $p(x)$ is divided by $g(x) = 2 - 3x$,we set $g(x) = 0$:$2 - 3x = 0 \implies 3x = 2 \implies x = \frac{2}{3}$.Now,we evaluate $p\left(\frac{2}{3}ight)$:$p\left(\frac{2}{3}ight) = \left(\frac{2}{3}ight)^{3} - \left(\frac{2}{3}ight) + 1$$= \frac{8}{27} - \frac{2}{3} + 1$$= \frac{8 - 18 + 27}{27} = \frac{17}{27}$.Since the remainder is $\frac{17}{27} 
eq 0$,$p(x)$ is not a multiple of $g(x)$.

Check whether $p(x)$ is a multiple of $g(x)$ or not,where $p(x) = x^{3} - x + 1$ and $g(x) = 2 - 3x$.

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