1. **State the problem:** We are given a cubic polynomial $$x^3 + 2x^2 + kx + 6$$ and told that $$(x + 2)$$ is a factor. We need to find the value of $$k$$. 2. **Recall the Factor Theorem:** If $$(x + 2)$$ is a factor of the polynomial, then substituting $$x = -2$$ into the polynomial should give zero. 3. **Apply the Factor Theorem:** Substitute $$x = -2$$ into $$x^3 + 2x^2 + kx + 6$$: $$(-2)^3 + 2(-2)^2 + k(-2) + 6 = 0$$ 4. **Simplify the expression:** $$-8 + 2(4) - 2k + 6 = 0$$ $$-8 + 8 - 2k + 6 = 0$$ $$6 - 2k = 0$$ 5. **Solve for $$k$$:** $$6 = 2k$$ $$k = \frac{6}{2} = 3$$ **Final answer:** $$k = 3$$