1. Let's start by understanding the problem: factoring by GCF means finding the Greatest Common Factor (GCF) of all terms in an expression and then factoring it out. 2. The formula or rule is: For an expression like $ax + ay$, the GCF is $a$, so you write it as $a(x + y)$. 3. Important rule: The GCF is the largest factor that divides all terms without leaving a remainder. 4. Example: Factor $12x^3 + 18x^2$ by GCF. 5. Find the GCF of coefficients 12 and 18, which is 6. 6. Find the GCF of variables $x^3$ and $x^2$, which is $x^2$ (the smallest power). 7. So, the GCF is $6x^2$. 8. Factor out $6x^2$: $$12x^3 + 18x^2 = 6x^2(\cancel{2x} + \cancel{3})$$ 9. Simplify inside the parentheses: $$6x^2(2x + 3)$$ 10. This is the factored form by GCF. Factoring by GCF helps simplify expressions and solve equations more easily.