Simplifying the polynomial gives:
(x² + 3x + 9)/(x³ + 6x² + 18x + 27)
How to carry out polynomial division?
(x³ - 27) ÷ (x⁴ + 3x³ - 27x - 81)
Factoring (x³ - 27) gives us:
(x - 3)(x² + 3x + 9)
Factorizing (x⁴ + 3x³ - 27x - 81) gives:
(x - 3)(x³ + 6x² + 18x + 27)
Thus:
(x³ - 27) ÷ (x⁴ + 3x³ - 27x - 81) = [(x - 3)(x² + 3x + 9)]/[(x - 3)(x³ + 6x² + 18x + 27)]
= (x² + 3x + 9)/(x³ + 6x² + 18x + 27)