94th Problem 2016

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:

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