Just a simple question (if you know the answer...)
Is it always possible to decompose a cubic real polynomial in 3 factors of degree one each or in two factor of degree one and two, using only basic operations and n-roots?
I know about Cardano's formula, but my question is a little bit more subtle.
If the polynomial has only one real root, you can find it using Cardano's formula. Then you can easily find the other polynomial by division.
But if you have three real roots, in Cardano's formula you need to calculate the cubic root of a complex number, which, as far as I know, need trigonometric functions to obtain explicit values of the real and imaginary part.
Thanks for any insight on this problem