Step 1

Let's understand the factor theorem before we get into solving the question directly.

(x - a) is a factor of f(x) if and only if f(a) = 0

Step 2

In our case, \(f(x) = x^{n}-c^{n}\)

Basis factor theorem, (x - c) will be a factor of \(f(x) = x^{n}-c^{n}\) if and only if f(c) = 0

Let's check:

\(f(c) = c^{n} - c^{n} = 0\)

Step 3

Hence, f(c) = 0

Hence, (x - c) is a factor of \(x^{n}-c^{n}\)

Let's understand the factor theorem before we get into solving the question directly.

(x - a) is a factor of f(x) if and only if f(a) = 0

Step 2

In our case, \(f(x) = x^{n}-c^{n}\)

Basis factor theorem, (x - c) will be a factor of \(f(x) = x^{n}-c^{n}\) if and only if f(c) = 0

Let's check:

\(f(c) = c^{n} - c^{n} = 0\)

Step 3

Hence, f(c) = 0

Hence, (x - c) is a factor of \(x^{n}-c^{n}\)