1. **State the problem:** Factor the quadratic expression $x^2 + 14x + 24$. 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, $a=1$, $b=14$, and $c=24$. We need two numbers that multiply to $1 \times 24 = 24$ and add to $14$. 4. **Find the numbers:** The pair $2$ and $12$ satisfy this because $2 \times 12 = 24$ and $2 + 12 = 14$. 5. **Rewrite the middle term:** $$x^2 + 2x + 12x + 24$$ 6. **Group terms:** $$(x^2 + 2x) + (12x + 24)$$ 7. **Factor each group:** $$x(x + 2) + 12(x + 2)$$ 8. **Factor out the common binomial:** $$(x + 12)(x + 2)$$ **Final answer:** The factored form is $$\boxed{(x + 12)(x + 2)}$$.