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 the 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 are $-2$ and $-3$ because $-2 \times -3 = 6$ and $-2 + (-3) = -5$. 5. **Write the factored form:** Using these numbers, the factorization is $$(x - 2)(x - 3).$$ 6. **Verify:** Expanding $(x - 2)(x - 3)$ gives $x^2 - 3x - 2x + 6 = x^2 - 5x + 6$, confirming the factorization is correct. **Final answer:** $$(x - 2)(x - 3).$