Find the remainder when

$f(x)=2x^3-3x^2+x-15$

is divided by $x-3$ .

The answer is 15.

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From the remainder factor theorem , we know that the remainder when a polynomial is divided by $x-a$ is given by $f(a)$ , thus the remainder when the given function is divided by $x-3$ will be:

$\begin{aligned} f(3)&=2(3^3)-3(3^2)+3-15\\ &=27-12\\ &=\boxed{15}\\ \end{aligned}$