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What is the remainder when [math]x^{1999}[/math] is divided by [math](x^2-1)[/math] ?
Yes, I know how to do long division of polynomials. Can you show me your steps?
The first step is to divide the leading term of [math]x^{1999}[/math] by the leading term of [math]x^2-1[/math]. This gives us [math]x^{1997}[/math]. We then multiply [math]x^{1997}[/math] by [math]x^2-1[/math] to get [math]x^{1999}-x^{1997}[/math]. We then subtract [math]x^{1999}-x^{1997}[/math] from [math]x^{1999}[/math] to get [math]x^{1997}[/math]. Repeat these steps until we get a remainder. In this case, the remainder is [math]1[/math].