93rd 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 $x-2$ will be:

$\begin{aligned} f(2)&=5(2^4)-2(2^3)+3(2^2)+2-32\\ &=64+14-32\\ &=32+14\\ &=\boxed{46}\\ \end{aligned}$