Algebra 2
posted by Donielle .
Look at the following polynomials and their factorizations:
x^21=(x1)(x+1)
x^31=(x1)(x^2+x+1)
x^41=(x1)(x^3+x^2+x+1)
In general, how can x^n1 be factored. Show that this factorization works by multiplying the factors

It should be obvious from the examples that
x^n  1 =
(x1)[x^(n1) + x^(n2) .. x + 1]
The series in the second factor stops when the last term => x^0 = 1