Let f(x) = x^{10}+5x^9-8x^8+7x^7-x^6-12x^5+4x^4-8x^3+12x^2-5x-5-x^10-5x^9+8x^8-7x^7+x^6+12x^5-4x^4+8x^3-12x^2.
Without using long division (which would be horribly nasty!), find the remainder when f(x) is divided by x^2-1.
