1. **Problem:** Factor the cubic expression $x^3 + 8$ completely. 2. **Formula and rules:** This is a sum of cubes, which factors as: $$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$ where $a = x$ and $b = 2$ because $8 = 2^3$. 3. **Apply the formula:** $$x^3 + 8 = x^3 + 2^3 = (x + 2)(x^2 - x \cdot 2 + 2^2)$$ 4. **Simplify inside the second factor:** $$x^2 - 2x + 4$$ 5. **Final factored form:** $$(x + 2)(x^2 - 2x + 4)$$ This matches option A. **Answer:** (x + 2)(x^2 - 2x + 4)