I am having trouble finding info on how to factor polynomials in ring of integers modulo powerful number.
For example: $x^2 - 1$ in $\textbf Z_{8}$.
I know by tinkering around that $(x - 1)(x + 1)$ and $(x - 3)(x + 3)$ are the factorizations, but I don't know how to factor polynomials in ring of integers modulo powerful number in general, which would have helped me solve this particular one much more quickly.