1. Let's start by stating the problem: How to factor an algebraic expression. 2. Factoring means rewriting an expression as a product of simpler expressions. 3. The most common methods include factoring out the greatest common factor (GCF), factoring trinomials, difference of squares, and factoring by grouping. 4. For example, to factor $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 5. Another example is difference of squares: $a^2 - b^2 = (a - b)(a + b)$. 6. Always check if there is a GCF first and factor it out. 7. Example: Factor $6x^2 + 9x$. 8. Step 1: Find GCF of 6 and 9, which is 3, and also $x$ is common. 9. Step 2: Factor out $3x$: $$6x^2 + 9x = 3x(\cancel{2x} + \cancel{3})$$ 10. So the factored form is $3x(2x + 3)$. 11. This process applies similarly to more complex expressions by identifying patterns and applying appropriate factoring techniques.