(x^{n}-a^{n}) is divisible by (x-a) where x \neq a, for <strong>EVERY</strong>
- A. natural number n ✓
- B. even natural number n only
- C. odd natural number n only
- D. prime number n only
Correct Answer: A. natural number n
Explanation
By standard algebraic identities, (x^n - a^n) = (x-a)(x^{n-1} + x^{n-2}a + \dots + a^{n-1}). This expansion is universally valid for any positive integer (natural number) n.
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