I hope someone can help provide elaboration on the homework question that I'm faced with, and why the solution is what it is.
The homework question is as follows:
Determine a general rules to help decide whether x - a and x + a are factors of x^n - a^n and x^n + a^n.
The homework solution is as follows:
- For x^n - a^n, if n is even, they're both factors.
- If n is odd, only x - a is a factor. For x^n + a^n, if n is even, neither is a factor.
- If n is odd, only x + a is a factor.