I have a to divide a thrid degree polynomial by another one, is it possible for me to get another polynomial out of it?
By the way, I am working with decimal numbers (floats in 32bits).
If it is possible, this problem needs to be solved relatively quickly as I plan on using the solution in a videogame, basically every frame. Let's say the division looks something like this: $$\frac{ax^3+bx^2+cx+d}{ex^3+fx^2+gx+h}$$ How would you get a polynomial out of it? Any suggestion is appreciated, thanks in advance.
EDIT: So it seems like my problem wasn't properly explained what i wanted is to get h(x) where $$h(x) =\frac{ax^3+bx^2+cx+d}{ex^3+fx^2+gx+h}$$ written as $$h(x) = jx^3+kx^2+lx+m$$ (or get a higher degree polynomial).
However, as @no lemon no melon said, it turns out that the result of the division of polynomials is not a polynomial but rather a rational function. So I guess that my question was "is the result of a polynomial division a polynomial?".
This is really new to me so hopefully this didn't seemed too stupid, again thanks a lot.
Suppose $\frac{f}{g}$ gives you a polynomial $h$ of degree $k$.
If degree of $f$ is $3$ and degree of $g$ is $3$.
Then we have $f=gh$. Degree of $f$ is equal to the degree of $g$ plus the degree of $h$.
Hence degree of $h$ must be $0$, the constant polynomial.