Final answer:
The leading coefficient of the polynomial 2x^4 - 9x^5 - x^3 + 9x^2 - 2 is -9, which is the coefficient of the highest power term.
Step-by-step explanation:
The leading coefficient of a polynomial is the coefficient of the term with the highest power of the variable when the polynomial is written in standard form, that is, ordered from the highest to the lowest powers of the variable. In the polynomial 2x^4 - 9x^5 - x^3 + 9x^2 - 2, the term with the highest power of x is -9x^5. Therefore, the leading coefficient of this polynomial is -9.