Check whether $p(x)$ is a multiple of $g(x)$ or not, where
$p(x)=x^{3}-x+1, \quad g(x)=2-3 x$
Check whether $p(x)$ is a multiple of $g(x)$ or not, where
$p(x)=x^{3}-x+1, \quad g(x)=2-3 x$
$p(x)$ will be a multiple of $g(x)$ if $g(x)$ divides $p(x)$
Now, $\quad g(x)=2-3 x=0$ gives $x=\frac{2}{3}$
Remainder $=p\left(\frac{2}{3}\right)=\left(\frac{2}{3}\right)^{3}-\left(\frac{2}{3}\right)+1$
$=\frac{8}{27}-\frac{2}{3}+1=\frac{17}{27}$
since remainder $\neq 0,$ So, $p(x)$ is not a multiple of $g(x)$.
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