P-irreducibility of binding polynomials

The problem of deciding whether a polynomial of positive coefficients can be factored into polynomials of the same type is important for studying many physiological processes. An efficient method to decide positive irreducibility is highly valuable. The known criteria for positive irreducible polynomials need to know root location first. Here, we present a new criterion for positive polynomials of degree 3 or 4, which can be expressed only by the coefficients of the given polynomials.