Factorization of polynomials

Given a polynomial with integer coefficients, how can I consider it as a polynomial with coefficients in other fields?

For example, let f be an integer polynomial. Can we obtain the factorization of f in other fields (e.g. finite fields)?’ Let us start with the following code:

> Z<x>:=PolynomialRing(Integers());
> f := x^2-3*x+5;
> F<x>:=PolynomialRing(FiniteField(3));
> g := F!f;
x^2 + 2

Therefore whenever makes sense to consider f with coefficients in another ring, then g will be the resulting polynomial.

For the other question:

> Factorisation(f);
[
    <x^2 - 3*x + 5, 1>
]
> Factorisation(g);
[
    <x + 1, 1>,
    <x + 2, 1>
]

This means that the polynomial f is irreducible over the integers, and g factors into (x + 1)(x + 2) over the field of three elements.