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. **Write the factors:** The quadratic factors as $(x + 2)(x + 3)$. 6. **Verify by expansion:** $(x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6$. **Final answer:** $$x^2 + 5x + 6 = (x + 2)(x + 3)$$