Can I prove that this polynomial is irreducible? The task is prove that the next polynomial us irreducible in $\mathbb{Q}$
$$y^3-3y +1 = 0.$$
I don't know the easy form for attack other problems similar.
thanks, 

Suppose that $y^3-3y+1$ is not irreducible over $\mathbb Q$. Then it can be factored into a linear and a quadratic term over $\mathbb Q$. Thus it has a rational root (the root of the linear term). Yet by the rational root theorem, any rational root of $y^3-3y+1$ is $\pm 1$ and it is straightforward to check that neither of these works.
