Final answer:
Polynomial functions have non-negative degrees, based on the definition, and these degrees represent the highest exponent on the variable in the polynomial. Negative degrees are not applicable to polynomials; they are related to different types of functions like rational functions.
Step-by-step explanation:
Polynomial functions are mathematical expressions involving a sum of powers of the variable, usually written as x. Each term in a polynomial is of the form anxn, where an is a coefficient and n is the degree of the term. The degree of the polynomial is the highest degree of its terms when the polynomial is expressed in its standard form.
By definition, the degree of a polynomial is non-negative, which means it must be zero or a positive integer. A polynomial cannot have a negative degree because the degree represents the highest power of x in the polynomial, and there is no such thing as a negative exponent in a polynomial function. Regular exponents in a polynomial denote multiplication of the base (variable x) by itself; a negative exponent would instead imply division, which leads us to a different class of functions altogether, such as rational functions.
In summary, while you might encounter negative exponents in other types of mathematical expressions, within the context of polynomial functions, degrees are always non-negative.