Find the remainder when

$f(x)=5x^4-2x^3+3x^2+x-32$

is divided by $x-2$ .

The answer is 46.

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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 $x-2$ will be:

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