1. **Problem statement:** Factorize the given expression. Since no specific expression was provided, let's consider a general example: factorize $x^2 - 5x + 6$. 2. **Formula and rules:** To factorize a quadratic expression $ax^2 + bx + c$, find two numbers that multiply to $ac$ and add to $b$. 3. **Intermediate work:** For $x^2 - 5x + 6$, $a=1$, $b=-5$, $c=6$. We need two numbers that multiply to $1 \times 6 = 6$ and add to $-5$. 4. The numbers are $-2$ and $-3$ because $-2 \times -3 = 6$ and $-2 + -3 = -5$. 5. **Factorization:** Rewrite the middle term using these numbers: $$x^2 - 2x - 3x + 6$$ Group terms: $$(x^2 - 2x) - (3x - 6)$$ Factor each group: $$x(x - 2) - 3(x - 2)$$ Factor out the common binomial: $$(x - 3)(x - 2)$$ 6. **Answer:** The factorized form of $x^2 - 5x + 6$ is $$(x - 3)(x - 2)$$.