Let's determine $m$ and $n$ such that

$$
x^{4}-3 x^{3}+m x+n
$$

is divisible by

$$
x^{2}-2 x+4
$$

expression.
The remainder of the division

$$
(m-8) x+24+n
$$

is zero for all values of $x$ if and only if

$$
m=8 \quad \text { and } \quad n=-24 \text {. }
$$