2024 · Q47
Let k be a positive integer. What is the quotient when x⁸ᵏ⁺³+x⁸ᵏ⁺⁶+x⁸ᵏ⁺⁹+x^(8k+12) is divided by (1 + x³) (1 + x⁶)?
Elementary MathematicsAlgebra
- Ax8k
- Bx8k+1
- Cx8k+2
- Dx8k+3
Explanation
Factor out x^(8k+3): the numerator is x^(8k+3)(1 + x³ + x⁶ + x⁹). The divisor (1+x³)(1+x⁶) expands to exactly 1 + x³ + x⁶ + x⁹. Cancelling gives quotient x^(8k+3) — option D.