Factor x^n - 1 for n = 6, 7, 8,..., 22.
Do I need to show the answer for each n? What is the proper way to show this?
[I'm assuming that you are looking for factorisations where the coefficients are rational numbers. If you're working over the complex numbers then you can factorise into n linear factors. If you are doing it over the real numbers then you can get a factorisation into linear and quadratic factors (but that is just as hard as doing it over the complex numbers).]