On some classes of irreducible polynomials

One of the fundamental tasks Symbolic Computation is factorization polynomials into irreducible factors. The aim paper to produce new families polynomials, generalizing previous results in area. example our general result that for a near-separated polynomial, i.e., form F(x,y)=f1(x)f2(y)−f2(x)f1(y), then F(x,y)+r always any constant r different from zero. We also provide biggest known family HIP several variables. These are p(x1,…,xn)∈K[x1,…,xn] over zero characteristic field K such p(h1(x1),…,hn(xn)) every n-tuple h1(x1),…,hn(xn) non one variable K. can be applied fields positive characteristic, with some modifications.