I would like to try to implement a factorization method for polynomials with integer coefficients which returns the irreducible factors. I read about Zassenhaus, LLL, van Hoeij algorithms but they all seem to be an overkill for what I try to do (which is learning the basics).
Could someone please suggest a simpler alternative? Preferably one without lifting, modular arithmetic, lattices, ... Ideally, I would be interested in the literature describing it or another implementation.