Question

Show that x-m is a factor of x^a-m^a

Answer 1

Welcome to OpenStudy!

First, you might show that x-m is a factor of x-m. x-m divided into x-m results in 1:
x-a
------- = 1
x - a

Next, show that x-m is a factor of x^a-m^a. Using long division, divide x-m into x^a-m^a. You could also do this using synthetic division.

____________
x-m | x^2 - m^2

Next, show that x-m is a factor of x^3 - m^3.

And so on.

You should see that a pattern emerges as you begin with a=1, move on to a=2, a=3, and so on.

Answer 2

use the fact that if \((x-m)\) is a factor of \(f(x)\) then this implies that \(f(m)=0\)

in your case \(f(x)=x^a-m^a\)