Final answer:
To factor out the greatest common factor of the polynomial expression, we find the common factors of the coefficients and variables. The greatest common factor is 9x^7y^2.
Step-by-step explanation:
To factor out the greatest common factor of the polynomial expression -9x8y2 - 27x7y11, we first need to find the common factors of the coefficients -9 and -27, as well as the variables x and y.
The greatest common factor of -9 and -27 is 9. The greatest common factor of x8 and x7 is x7. The greatest common factor of y2 and y11 is y2.
So, the greatest common factor of the polynomial expression is 9x7y2.