1. The problem is to factorize the expression $x^2 - 5x + 6$. 2. The formula used for factorization of a quadratic expression $ax^2 + bx + c$ is to find two numbers that multiply to $ac$ and add to $b$. 3. Here, $a=1$, $b=-5$, and $c=6$. We need two numbers that multiply to $6$ and add to $-5$. 4. The numbers are $-2$ and $-3$ because $-2 \times -3 = 6$ and $-2 + (-3) = -5$. 5. So, the factorization is $x^2 - 5x + 6 = (x - 2)(x - 3)$. 6. This means the expression can be written as the product of two binomials $(x - 2)$ and $(x - 3)$. Final answer: $(x - 2)(x - 3)$.