Question

Factorize \(a^k - b^k\) by using synthetic division.

Answer 1

\[P(a)=a^k - b^k\]\[P(b)=b^k - b^k=0\]so we can divide by \(a-b\)

Answer 2

man sorry i have internet difficulties here

Answer 3

I got that factor but am not sure the way to do synthetic division
I did it this way:

So, \[(a^k - b^k ) = (a-b) (a^{k-1} + a^{k-2}b+ ... + b^{k-1})\]Does it make sense?

PS: I'm not man :P