On the irreducible factors of a polynomial.

In 2013, S. H. Weintraub proved a generalization of the classical Eisenstein irreducibility criterion by providing a bound on the degrees of factors of a polynomial with integer coefficients (see [Proc. Amer. Math. Soc. 141(4) (2013), pp. 1159-1160]). In this paper, we extend this result with a much weaker hypothesis in a more general setup for polynomials having coefficients from the valuation ring of arbitrary valued field. Moreover, when a polynomial f(x) has coefficients from the valuation ring of a henselian valued field K, then we give more precise information about an irreducible factor of f(x) over K. [ABSTRACT FROM AUTHOR]