Question

Use a Factor Theorem to prove that x+c is a factor of x^n+c^n for any positive odd integer n.

Answer 1

\[f(x)=x^n+c^n\] , \(n\) is odd
what is
\[f(-c)\]?

Answer 2

= 0

Answer 3

@satellite73

Answer 4

dat sit!! f(-c) =0 shows -c is a root of f(x) for all n odd. Or, f(x) can be factored as \((x+c) (x^{n-1}-........)\)