Final answer:
The given polynomial 3x² + 2x⁴ - 4x⁵ - 1 is classified as a quintic polynomial because the term with the highest exponent is -4x⁵, indicating it is of the fifth degree.
Step-by-step explanation:
To classify the polynomial 3x² + 2x⁴ - 4x⁵ - 1 based on its degree, we need to look for the term with the highest exponent. In this polynomial, the term with the highest exponent is -4x⁵. The exponent here is 5, which means the polynomial is of the fifth degree. Therefore, the correct classification for this polynomial is C) Quintic.
Polynomials are classified based on their highest degree term. A quadratic equation, for example, is a polynomial of degree 2 and has the general form ax² + bx + c = 0. However, our given polynomial has a term of degree 5, which makes it a quintic polynomial, not a quadratic, cubic, or 11th degree polynomial.