I wonder whether the question whether a polynomial in $\mathbb Q[x]$ is irreducible over $\mathbb Q$ is easier if all coefficients are non-negative.
I found various sufficient conditions for a polynomial to be irreducible in the internet, but besides Cohn's criterion (See https://en.wikipedia.org/wiki/Cohn%27s_irreducibility_criterion ) which can only be applied in very special cases, I did not find criterions that make use of the case that all the coefficients are non-negative.
Is the computational complexity to determine whether a polynomial in $\mathbb Q[x]$ is irreducible over $\mathbb Q$ lower if all the coefficients are non-negative ?