Question

For n N, xⁿ⁺¹ + (x+1)²n-1 is divisible by:

• A. x
• B. x+1
• C. x² + x + 1
• D. x² - x + 1

Hint:

Use cube roots of unity to test divisibility by x²+x+1.

Answer 1

The Correct Option is C

Step 1: Substitution method. Put x = ω, a cube root of unity.
Step 2: Evaluation. Expression becomes zero, hence divisible by x² + x + 1.