On polynomial long division

Question

What happens when the dividing polynomial has a higher degree? Let $f$ and $g$ be two polynomials so that $\deg(g)>\deg(f)$. What will be the result of $r,q$ for $f/g$? Or a more specific example: $$(x^3-5x^2+6x-3)/(x^4-8x^2+2)$$

Answer 1

$$f(x) = 0\,g(x) + f(x)$$

$r=f, q=0$

It is similar to what do we get when we divide $2$ by $5$,

$$2=0\cdot 5 + 2$$

$q=0, r=2$.