1. **State the problem:** We are given a cubic polynomial $$x^3 + 4x^2 - kx - 2$$ and told that $$x - 1$$ is a factor of this polynomial. We need to find the value of $$k$$. 2. **Recall the Factor Theorem:** If $$x - a$$ is a factor of a polynomial $$f(x)$$, then $$f(a) = 0$$. 3. **Apply the Factor Theorem:** Since $$x - 1$$ is a factor, substitute $$x = 1$$ into the polynomial and set it equal to zero: $$1^3 + 4(1)^2 - k(1) - 2 = 0$$ 4. **Simplify the expression:** $$1 + 4 - k - 2 = 0$$ $$3 - k = 0$$ 5. **Solve for $$k$$:** $$k = 3$$ **Final answer:** $$k = 3$$