Factor Gcf D867Dc

1. **State the problem:** Factor out the greatest common monomial factor from the polynomial $$11y^3 - 22y^2 + 11y^2$$. 2. **Identify the terms:** The polynomial has three terms: $$11y^3$$, $$-22y^2$$, and $$11y^2$$. 3. **Find the greatest common factor (GCF) of the coefficients:** The coefficients are $$11$$, $$-22$$, and $$11$$. - The GCF of $$11$$, $$22$$, and $$11$$ is $$11$$. 4. **Find the GCF of the variable parts:** The variable parts are $$y^3$$, $$y^2$$, and $$y^2$$. - The smallest power of $$y$$ among the terms is $$y^2$$. 5. **Therefore, the greatest common monomial factor is:** $$11y^2$$. 6. **Factor out $$11y^2$$ from each term:** $$11y^3 - 22y^2 + 11y^2 = 11y^2(\frac{11y^3}{11y^2} - \frac{22y^2}{11y^2} + \frac{11y^2}{11y^2})$$ 7. **Simplify each term inside the parentheses:** $$= 11y^2(y - 2 + 1)$$ 8. **Combine like terms inside the parentheses:** $$= 11y^2(y - 1)$$ **Final answer:** $$11y^2(y - 1)$$