1. **State the problem:** Rewrite the polynomial $12a^2b^4 - 36a^2b + 44abc$ as the product of a monomial and a polynomial. 2. **Identify the greatest common factor (GCF):** - For the coefficients: GCF of 12, 36, and 44 is 4. - For the variables: All terms have at least one $a$, so $a$ is common. - For $b$: The terms have $b^4$, $b$, and $b^1$ respectively, so the smallest power is $b^1$. Thus, the GCF is $4ab$. 3. **Factor out the GCF:** $$12a^2b^4 - 36a^2b + 44abc = 4ab(\cancel{3a b^3} - \cancel{9a} + \cancel{11c})$$ Here, we divided each term by $4ab$: - $\frac{12a^2b^4}{4ab} = 3a b^3$ - $\frac{36a^2b}{4ab} = 9a$ - $\frac{44abc}{4ab} = 11c$ 4. **Write the final factored form:** $$4ab(3ab^3 - 9a + 11c)$$ This expresses the original polynomial as the product of the monomial $4ab$ and the polynomial $3ab^3 - 9a + 11c$.