1. **State the problem:** Factor the cubic polynomial expression $$24x - 2x^2 - 2x^3$$ completely. 2. **Write the polynomial:** $$24x - 2x^2 - 2x^3$$ 3. **Identify the greatest common factor (GCF):** Each term has a factor of $$2x$$. 4. **Factor out the GCF:** $$24x - 2x^2 - 2x^3 = 2x(\cancel{12} - \cancel{x} - \cancel{x^2})$$ 5. **Simplify inside the parentheses:** $$2x(12 - x - x^2)$$ 6. **Rewrite the quadratic inside the parentheses:** $$12 - x - x^2 = -x^2 - x + 12$$ 7. **Factor the quadratic:** Multiply by -1 to make the leading coefficient positive: $$-(x^2 + x - 12)$$ 8. **Factor the quadratic inside:** Find two numbers that multiply to $$-12$$ and add to $$1$$ (coefficient of $$x$$): These are $$4$$ and $$-3$$. 9. **Write the factorization:** $$x^2 + x - 12 = (x + 4)(x - 3)$$ 10. **Put it all together:** $$2x(-(x + 4)(x - 3)) = -2x(x + 4)(x - 3)$$ **Final answer:** $$\boxed{-2x(x + 4)(x - 3)}$$