As I understand it $x^5 - x + 1$ is not solvable by radicals. But it splits over $\mathbb{C}$, so how does it factor into linear factors?
2026-04-13 16:17:48.1776097068
How to factor $x^5 - x + 1$
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By Descartes' Rule of Signs, there is one real root. Find it. The result will give you a product of a linear factor times a quartic, which can be solved by radicals. You may also use Jacobi theta functions to find the roots, since it is in Bring's (reduced) form.