Factor Polynomial A8C873

1. **State the problem:** Factor the polynomial $$15a - 15a^2$$ using the greatest common factor (GCF). 2. **Identify the GCF:** The terms are $$15a$$ and $$15a^2$$. - The numerical GCF of $$15$$ and $$15$$ is $$15$$. - The variable part common to both terms is $$a$$ (since $$a^1$$ and $$a^2$$ share $$a^1$$). - Therefore, the GCF is $$15a$$. 3. **Factor out the GCF:** $$15a - 15a^2 = 15a(\frac{15a}{15a} - \frac{15a^2}{15a})$$ 4. **Simplify inside the parentheses:** $$= 15a(1 - \cancel{15a}/\cancel{15a} \times a) = 15a(1 - a)$$ 5. **Final factored form:** $$15a - 15a^2 = 15a(1 - a)$$ This means the polynomial is factored by taking out the greatest common factor $$15a$$ and leaving the remaining terms inside the parentheses.