Question

the factor theorem states: let c be any real number and f some polynomial function. then (x-c) is a factor of f(x) if and only if f(c)=0. use the factor thearom to prove that (x-c) is a factor of x^n-c^n for any positive integer n.

Answer 1

Consider that:\[
f(c) = (c)^n-c^n = 0
\]

Answer 2

Due to \(n\) being a positive integer, we know that \(f(x)\) is a polynomial.