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, 

I guess you mean irreducible over $\mathbb Q$. If $y^3-3y+1=0$ were reducible then it could be written as a product of either tree linear factors or as a product of one linear factor and a quadratic factor. In either case it would have a rational root. You can check that it does not have rational roots using the rational root test.
