Understanding modulos and polynomials when dividing two polynomials I understand the idea of modulo with integers but I am having an incredibly hard time wrapping my head around the idea of modulus with polynomials. I am taking a course in which I need to divide polynomials in terms of a specific modulus. I am able to divide the polynomials but don't understand how the mod applies. 
So for example, $f(x)$=$$4x^4+2x^3+6x^2+4x+5$$ and $g(x)$=$$3x^2+2$$ and I am asked to divide f(x) by g(x) in mod 7.

All you need is computing the inverse of the leading coefficient modulo $7$. The operations are the same as in $\mathbf R$, but you compute modulo $7$. Here is an example:

