I am reading Fulton's book "Algebraic Curves" and I'd like to see how are solved exercises 2.34 and 2.35. They say:
1) Factor Y^2-2XY^2 + X^3 into linear factors in C[X,Y] (where C denotes complex numbers).
Just above it is stated that: "Up to powers of X_{n+1}, factoring a form F \in R[X_1, . . . ,X_{n+1}] is the same as
factoring F \in R[X_1, . . . ,X_n]. In particular, if F \in k[X,Y ] is a form, k algebraically closed, then F factors into a product of linear factors."
It must be helpful... but I don't know how to use it. And also, "linear factors" in C[X,Y] are of the form X-aY?

Thank you for your help.