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stfz

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## Homework Statement

Prove that ##(a-b)## is a factor of ##a^5-b^5##, and find the other factor.

## Homework Equations

Remainder theorem : remainder polynomial ##p(x)## divided by ##(x-a)## is equal to ##p(a)##

Factor theorem : if remainder = 0, then divisor was a factor of dividend.

## The Attempt at a Solution

I

*think*am able to prove that it is a factor:

##P(x) = x^5 - b^5##; we replace a with x

##P(x) = (x-b)Q(x) + 0## ; we assume that (x-b) is a factor

##P(b) = (b-b)Q(x) + 0 = 0 ##; proves that .. um.. I think I'm going the wrong way anyway. This doesn't really prove anything? er.. eh.. ?

And I can't really find the other factor

I could do most of the other questions in the exercise, but not this one (and other related ones!)

Any help would be appreciated

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