Factor out the greatest common factor from the following polynomial. \[ 33 x^{5} y^{5}-22 x^{4} y^{5} \]

To factor out the greatest common factor (GCF) from the polynomial \( 33 x^{5} y^{5} - 22 x^{4} y^{5} \), we first determine the GCF of the coefficients and the variables. The coefficients are 33 and 22. The GCF of 33 and 22 is 11. Next, we look at the variable parts: - For \( x^5 \) and \( x^4 \), the GCF is \( x^4 \) (the lowest power). - For \( y^5 \) in both terms, since both terms have \( y^5 \), the GCF is \( y^5 \). Combining these, the overall GCF is \( 11 x^4 y^5 \). Now we factor this out from the polynomial: \[ 33 x^{5} y^{5} - 22 x^{4} y^{5} = 11 x^{4} y^{5} (3x - 2) \] So the factored form of the polynomial is: \[ 11 x^{4} y^{5} (3x - 2) \]