Final answer:
The greatest common factor of th z²,-z⁹ is z.
Step-by-step explanation:
To find the greatest common factor of the given expressions, we need to factorize each expression.
Factoring z², we get:
z² = z * z
Factoring -z⁹, we get:
-z⁹ = -z * z * z * z * z * z * z * z * z
Now, we can see that both expressions have a common factor of z. Therefore, the greatest common factor of z² and -z⁹ is z.