1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 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 our problem:** Here, $a=1$, $b=5$, and $c=6$. We need two numbers that multiply to $1 \times 6 = 6$ and add to $5$. 4. **Find the numbers:** The numbers $2$ and $3$ satisfy this because $2 \times 3 = 6$ and $2 + 3 = 5$. 5. **Rewrite the middle term:** $$x^2 + 5x + 6 = x^2 + 2x + 3x + 6$$ 6. **Group terms:** $$= (x^2 + 2x) + (3x + 6)$$ 7. **Factor each group:** $$= x(x + 2) + 3(x + 2)$$ 8. **Factor out the common binomial:** $$= (x + 3)(x + 2)$$ **Final answer:** $$\boxed{(x + 3)(x + 2)}$$