If the polynomial $f(x)=x^4- 6x^3+16x^2-25x+10$ is divided by another polynomial $q(x) = x^2-2x+k$, the reminder is $x+a$ . Find $k$ and $a$.

please don't solve it by long division as i am searching for some other approaches

my attempt : i thought $x^2-2x + k$ has two roots let say 
$m$ and $2-m$ then i tried to equate both sides by putting $m$ and $2-m$ in f(x) but i am not arriving at any answer please don't solve it by long division.