1. Stating the problem: We want to resolve the expression $$\frac{2x^2 + 7x + 33}{x^3 + 0x^2 - 11x}$$. 2. Simplify the denominator: The denominator is $$x^3 + 0x^2 - 11x = x^3 - 11x$$. We can factor out an $$x$$: $$x^3 - 11x = x(x^2 - 11)$$. 3. Factor the numerator if possible: The numerator is $$2x^2 + 7x + 33$$. Try the quadratic formula or factorization: The discriminant $$\Delta = 7^2 - 4 \cdot 2 \cdot 33 = 49 - 264 = -215 < 0$$. Since the discriminant is negative, the numerator has no real factors; it remains as is. 4. Write the expression with factored denominator: $$\frac{2x^2 + 7x + 33}{x(x^2 - 11)}$$. 5. Final answer: The expression simplified as much as possible is $$\boxed{\frac{2x^2 + 7x + 33}{x(x^2 - 11)}}$$ with the denominator factored.