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