1. **State the problem:** Factor the quadratic expression $x^2 + 11x + 24$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 3. **Apply to this problem:** Here, $a=1$, $b=11$, and $c=24$. We need two numbers that multiply to $1 \times 24 = 24$ and add to $11$. 4. **Find the numbers:** The pair $3$ and $8$ satisfy this because $3 \times 8 = 24$ and $3 + 8 = 11$. 5. **Write the factored form:** $$x^2 + 11x + 24 = (x + 3)(x + 8)$$ 6. **Verify by expansion:** $$(x + 3)(x + 8) = x^2 + 8x + 3x + 24 = x^2 + 11x + 24$$ **Final answer:** $$\boxed{(x + 3)(x + 8)}$$