Re: polynomial question

On 28 Mar 2006 13:14:41 -0800, "LuckyOne" <gwlucky@xxxxxxxxxx> wrote:

x^n - 1 has root 1 how do you know that x-1 divides x^n-1 resulting in
another polynomial. Do you have to do long division ?

Long division will convince you. By the way more properly you should
say

x^n - 1 = 0

The solutions of this equation will lie on the unit circle in R^2 when
thought of as the complex plane. They will be evenly spaced by
360deg/n.

They need not do any such thing. The polynomial could be from some
commutative ring which has nothing to do with complex numbers. For
example, in Z_2[x] it has exactly one root for any n >= 1.
.

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