1. **Stating the problem:** We need to factorize a given algebraic expression. Since the user did not specify the expression, let's consider a common example: $$x^2 - 5x + 6$$. 2. **Formula and rules:** To factorize a quadratic expression of the form $$ax^2 + bx + c$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$. 3. **Intermediate work:** For $$x^2 - 5x + 6$$, $$a=1$$, $$b=-5$$, and $$c=6$$. 4. Find two numbers that multiply to $$1 \times 6 = 6$$ and add to $$-5$$. These numbers are $$-2$$ and $$-3$$. 5. Rewrite the middle term using these numbers: $$x^2 - 2x - 3x + 6$$ 6. Factor by grouping: $$x(x - 2) - 3(x - 2)$$ 7. Factor out the common binomial: $$(x - 3)(x - 2)$$ 8. **Final answer:** The factorization of $$x^2 - 5x + 6$$ is $$(x - 3)(x - 2)$$.