1. The problem is to solve an equation or simplify an expression using the factorization method. 2. Factorization involves expressing the given expression as a product of its factors. 3. First, identify common factors or apply special factorization formulas such as difference of squares, perfect square trinomials, or factoring trinomials. 4. Example: To factorize $x^2 - 5x + 6$, find two numbers that multiply to $6$ and add to $-5$, which are $-2$ and $-3$. 5. So, $x^2 - 5x + 6 = (x - 2)(x - 3)$. 6. Using this factorization, you can solve the equation $x^2 - 5x + 6 = 0$ by setting each factor to zero: $$x - 2 = 0 \implies x = 2$$ $$x - 3 = 0 \implies x = 3$$ 7. Hence, the solutions are $x = 2$ and $x = 3$. This demonstrates the factorization method for solving quadratic equations or simplifying expressions.