1. The problem is to factorize algebraic expressions. 2. To factorize means to write a given expression as a product of its factors. 3. Common methods include: taking out the greatest common factor (GCF), factoring trinomials, difference of squares, and grouping. 4. For example, to factorize $x^2 - 9$, recognize this as a difference of squares: $$x^2 - 9 = (x)^2 - (3)^2 = (x - 3)(x + 3)$$ 5. Another example, factorize $6x^2 + 9x$ by taking out the GCF 3x: $$6x^2 + 9x = 3x(2x + 3)$$ 6. Factorization simplifies expressions and solves equations by setting each factor to zero.