1. **State the problem:** We are given that $(x + 4)$ is a factor of the quadratic polynomial $x^2 - 3x + p$. We need to find the value of $p$. 2. **Recall the factor theorem:** If $(x + 4)$ is a factor of the polynomial, then substituting $x = -4$ into the polynomial should give zero. 3. **Apply the factor theorem:** Substitute $x = -4$ into $x^2 - 3x + p$: $$(-4)^2 - 3(-4) + p = 0$$ 4. **Simplify the expression:** $$16 + 12 + p = 0$$ $$28 + p = 0$$ 5. **Solve for $p$:** $$p = -28$$ **Final answer:** $p = -28$