Does the answer to this question
Proof of Cohn's Irreducibility Criterion
actually prove Cohn's sufficient irreducibility criterion ?
The criterion is as follows :
Suppose, $f(x)$ is a polynomial with non-negative integer coefficients and $b$ is a number larger than all the coefficients. If $f(b)$ is a prime number, then $f(x)$ is irreducible over $\mathbb Q[x]$.
If we assume, that $f(x)=g(x)\cdot h(x)$ and $f(b)$ is prime , then we have WLOG $g(b)=1$ and $h(b)$ is a prime number. I could not finish the proof and found a much simpler approach in the given link. But I am not sure whether the proof is actually valid. Who can approve or reject this proof ?