On 22/01/2008, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
> p: x^6+3*x^5+6*x^4+3*x^3+9*x+9;
> p2: factor(p,q^3-2)$
> solve(subst(q=2^(1/3),p2),x);
Sweet, I didn't know you could give hints to the factor function. Good to know.
As for those of you who offered numerical solutions, yes, there is no
general formula for a quintic or higher, but this wasn't a general
polynomial, but a very specific one. It's the minimal polynomial for
2^(1/3) + exp(2*%pi*%i/3) over the rationals. :-)
Thank you for your help,
- Jordi G. H.