1. **State the problem:** Factor the expression given by the user. Since no specific expression was provided, let's consider a general example: factor $x^2 - 5x + 6$. 2. **Formula and rules:** To factor a quadratic expression of the form $ax^2 + bx + c$, find two numbers that multiply to $ac$ and add to $b$. 3. **Intermediate work:** For $x^2 - 5x + 6$, $a=1$, $b=-5$, and $c=6$. 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:** $$x^2 - 5x + 6 = (x - 2)(x - 3)$$ 6. **Explanation:** We split the middle term using the two numbers found and factor by grouping: $$x^2 - 2x - 3x + 6 = x(x - 2) - 3(x - 2) = (x - 3)(x - 2)$$ 7. **Final answer:** The factored form is $$(x - 2)(x - 3)$$.