Let Y= (t,t²,t³) mid t in k be the twisted cubic curve. I'm trying to prove this curve is a variety, i.e., it's irreducible and affine algebraic set. The easier part is to prove the twisted cubic curve is an affine algebraic set (Y=Z(x²-y,x³-z)). I don't know how to prove that Y is irreducible, I'm trying to prove that (x²-y,x³-z) is prime, I think if I do this I proved what I want, but I found this hard to prove. I need help to finish this question. Thanks a lot.