1. **State the problem:** Factor the quadratic expression $X^2 + 7X + 12$. 2. **Recall the factoring formula:** For a quadratic $X^2 + bX + c$, we look for two numbers that multiply to $c$ and add to $b$. 3. **Identify $b$ and $c$:** Here, $b = 7$ and $c = 12$. 4. **Find two numbers:** We need two numbers whose product is $12$ and sum is $7$. These numbers are $3$ and $4$ because $3 \times 4 = 12$ and $3 + 4 = 7$. 5. **Write the factored form:** Using these numbers, the factorization is $$(X + 3)(X + 4).$$ 6. **Verify by expansion:** Expanding $(X + 3)(X + 4)$ gives $X^2 + 4X + 3X + 12 = X^2 + 7X + 12$, confirming the factorization is correct. **Final answer:** $$(X + 3)(X + 4)$$