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. **Rewrite the middle term:** $$x^2 + 3x + 8x + 24$$ 6. **Group terms:** $$(x^2 + 3x) + (8x + 24)$$ 7. **Factor each group:** $$x(x + 3) + 8(x + 3)$$ 8. **Factor out the common binomial:** $$(x + 8)(x + 3)$$ **Final answer:** The factored form of $x^2 + 11x + 24$ is $$\boxed{(x + 8)(x + 3)}$$.