1. **State the problem:** Factor the quadratic expression $x^2 + 9x + 18$. 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, $a=1$, $b=9$, and $c=18$. We need two numbers that multiply to $1 \times 18 = 18$ and add to $9$. 4. **Find the numbers:** The numbers $6$ and $3$ satisfy this because $6 \times 3 = 18$ and $6 + 3 = 9$. 5. **Write the factored form:** Using these numbers, the factorization is $$(x + 6)(x + 3).$$ 6. **Check by expansion:** Expanding $(x + 6)(x + 3)$ gives $x^2 + 3x + 6x + 18 = x^2 + 9x + 18$, confirming the factorization is correct. **Final answer:** $$(x + 6)(x + 3).$