A polynomial leaves remainder [math]2[/math] when divided by [math]x-1[/math] and remainder [math]1[/math] when divided by [math]x-2[/math]. If the polynomial is divided by [math](x-1)(x-2)[/math], then what would be the remainder?
Find the remainder when [math]x^{2007}[/math] is divided by [math]x^2-1?[/math]