What is the remainder when x100−1x^{100} - 1x100−1 is divided by x2−x−2x^2 - x - 2x2−x−2?
2100−13x+2101+13\frac{2^{100}-1}{3}x + \frac{2^{101}+1}{3}32100−1x+32101+1
2100−13x+2100+23\frac{2^{100}-1}{3}x + \frac{2^{100}+2}{3}32100−1x+32100+2
2100−13x+2100−23\frac{2^{100}-1}{3}x + \frac{2^{100}-2}{3}32100−1x+32100−2
2100+13x+2100−13\frac{2^{100}+1}{3}x + \frac{2^{100}-1}{3}32100+1x+32100−1