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 the rule:** 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. **Rewrite the middle term:** $x^2 + 6x + 3x + 18$. 6. **Group terms:** $(x^2 + 6x) + (3x + 18)$. 7. **Factor each group:** $x(x + 6) + 3(x + 6)$. 8. **Factor out the common binomial:** $(x + 6)(x + 3)$. **Final answer:** $$x^2 + 9x + 18 = (x + 6)(x + 3)$$