Question

factor x^(2012) - 1 using integer coefficients (and ellipses!)

Answer 1

x^(2012) - 1
=(x^1006+1)(x^1006-1)
=(x^1006+1)(x^503+1)(x^503-1)
=(x^2+1)(x^1004-x^1002+x^1000-...-x^2+1) (x+1)(x^502-x^501+x^500....-x+1) (x-1)(x^502+x^501+x^500+...+x^2+1)