On some classes of irreducible polynomials

One of the fundamental tasks of Symbolic Computation is the factorization of polynomials into irreducible factors. The aim of the paper is to produce new families of irreducible polynomials, generalizing previous results in the area. One example of our general result is that for a near-separated polynomial, i.e., polynomials of the form , then is always irreducible for any constant r different from zero. We also provide the biggest known family of HIP polynomials in several variables. These are polynomials over a zero characteristic field such that is irreducible over for every n-tuple of non constant one variable polynomials over . The results can also be applied to fields of positive characteristic, with some modifications.Peer ReviewedPostprint (author's final draft