sage: S.<x> = PolynomialRing(QQ)
sage: factor( x^15 - 1 )
(x - 1) * (x^2 + x + 1) * (x^4 + x^3 + x^2 + x + 1)
    * (x^8 - x^7 + x^5 - x^4 + x^3 - x + 1)
sage: R.<x> = PolynomialRing(GF(11))
sage: factor( x^15 - 1 )
(x + 2) * (x + 6) * (x + 7) * (x + 8) * (x + 10)
    * (x^2 + x + 1)
    * (x^2 + 3*x + 9) * (x^2 + 4*x + 5) * (x^2 + 5*x + 3) * (x^2 + 9*x + 4)
sage: factor(x^4 + x^3 + x^2 + x + 1)
(x + 2) * (x + 6) * (x + 7) * (x + 8)
sage: factor(x^8 - x^7 + x^5 - x^4 + x^3 - x + 1)
(x^2 + 3*x + 9) * (x^2 + 4*x + 5) * (x^2 + 5*x + 3) * (x^2 + 9*x + 4)

> Factorization((PolynomialRing(GF(11)))!(x^15-1));
[
    <x + 2, 1>,
    <x + 6, 1>,
    <x + 7, 1>,
    <x + 8, 1>,
    <x + 10, 1>,
    <x^2 + x + 1, 1>,
    <x^2 + 3*x + 9, 1>,
    <x^2 + 4*x + 5, 1>,
    <x^2 + 5*x + 3, 1>,
    <x^2 + 9*x + 4, 1>
]