Factorisation of Quintic x^5 - x + n into Irreducible Quadratic and Irreducible Cubic

Theorem
The quintic $x^5 - x + n$ can be factorized into the product of an irreducible quadratic and an an irreducible cubic $n$ is in the set:
 * $\set {\pm 15, \pm 22 \, 440, \pm 2 \, 759 \, 640}$

Proof
We have that:
 * $x^5 - x + 2 \, 759 \, 640 = \paren {x^2 + 12 x + 377} \paren {x^3 - 12 x^2 - 233 x + 7320}$