Can I get a polynomial out of a polynomial division?

[kantic]

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:
_{((ax3+bx3+cx+d)/(ex3+fx3+gx+h)) = f(x)}
How do i get _{f(x) = jx3+kx3+lx+m}?

 

[lookagain]

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:
_{((ax3+bx3+cx+d)/(ex3+fx3+gx+h)) = f(x)}
How do i get _{f(x) = jx3+kx3+lx+m}?

j, k, and l would have to be zero. m would be a constant. You would not
get another third degree polynomial out of it as the quotient for f(x).

 

[Dr.Peterson]

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:
_{((ax3+bx3+cx+d)/(ex3+fx3+gx+h)) = f(x)}
How do i get _{f(x) = jx3+kx3+lx+m}?

The degree of the quotient will be the difference in the degrees of the dividend and divisor. Given that the latter are the same, the quotient has to be a constant (and the remainder will in general have degree 2, less in special cases). Yes, it will be a polynomial (usually with a remainder), but not a very interesting one.

What were you expecting?

 

[JeffM]

Every product of polynomials is a polynomial, but not every quotient of polynomials is a polynomial.