1. The problem is to factor the quadratic expression $x^2 + 5x + 6$. 2. To factor a quadratic of the form $ax^2 + bx + c$, we look for two numbers that multiply to $c$ and add to $b$. 3. Here, $a=1$, $b=5$, and $c=6$. 4. We need two numbers that multiply to $6$ and add to $5$. These numbers are $2$ and $3$ because $2 \times 3 = 6$ and $2 + 3 = 5$. 5. Therefore, we can write the factorization as: $$x^2 + 5x + 6 = (x + 2)(x + 3)$$ 6. This is the factored form of the quadratic expression.