1. The problem asks: What is the degree of the polynomial $5z^3 - 2z^4 - 9z^2 + z$? 2. The degree of a polynomial is the highest power of the variable in the expression. 3. Identify the powers of $z$ in each term: - $5z^3$ has degree 3 - $-2z^4$ has degree 4 - $-9z^2$ has degree 2 - $z$ is $z^1$, degree 1 4. The highest degree among these is 4 from the term $-2z^4$. 5. Therefore, the degree of the polynomial is $\boxed{4}$.