1. **Problem:** Find the value of coefficient $A$ in the cubic polynomial $Ax^3 + 2x^2 + 3x - 2$ given that $(x + 1)$ is a factor. 2. **Formula and rule:** If $(x + 1)$ is a factor, then the polynomial evaluated at $x = -1$ must be zero. This is the Factor Theorem: $$P(-1) = 0$$ 3. **Substitute $x = -1$ into the polynomial:** $$A(-1)^3 + 2(-1)^2 + 3(-1) - 2 = 0$$ 4. **Simplify each term:** $$-A + 2 - 3 - 2 = 0$$ 5. **Combine like terms:** $$-A - 3 = 0$$ 6. **Solve for $A$:** $$-A = 3$$ $$A = -3$$ **Final answer:** The value of $A$ is $-3$.