1. **State the problem:** Factor the polynomial expression $$3x^4 - 24x$$. 2. **Identify the greatest common factor (GCF):** Both terms have a factor of $$3x$$. 3. **Factor out the GCF:** $$3x^4 - 24x = 3x(x^3 - 8)$$ 4. **Recognize the difference of cubes:** $$x^3 - 8 = x^3 - 2^3$$ 5. **Use the difference of cubes formula:** $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ 6. **Apply the formula:** $$x^3 - 2^3 = (x - 2)(x^2 + 2x + 4)$$ 7. **Write the fully factored form:** $$3x(x - 2)(x^2 + 2x + 4)$$ 8. **Check the options:** This matches option D. **Final answer:** $$3x(x - 2)(x^2 + 2x + 4)$$