I have the polynomial
Let be the splitting field of it.
How can I show that is divisible by 5.
Anyway, this may help : The Rational Roots Test
looking for rational solutions would have given the answer for a polynomial in of degree 2 or 3 (in such case, "no solution irreducibility"). With higher degrees, the polynomial can be a product of irreducible polynomials and be reducible without having ant root. But thanks
Stupid me >< I always miss that !