Suppose that is a zero of in some field extension of . Write as a product of linear factors in .
Since is a zero, is a factor of . My plan was to simply divide into to obtain a cubic and then find a root of the cubic, etc. until I obtained all the linear factors. Is there a reason that shouldn't divide ? I don't see one but it is not dividing it when I try. Does the fact that lies in and not affect this?