You have a point, but the definitions are that
a monomial has only one term,
a binomial has exactly two terms,
a trinomial has exactly three terms, and
a polynomial has at least one term.
Ususally polynomial is used when the number of terms is numerous, unknown or indefinite. It would be too restrictive if 1-3 terms are excluded from the definition.
why would something like y=x^-3 not be a polynomial function?
must the value of n always be nonnegetive?
Yes, the exponents have to be non-negative (i.e. zero allowed, thus constant terms) and integers. x2/3 and x-2 are not polynomials.
The definition of a polynomial, as per Wiki, is as follows:
"In mathematics, a polynomial is a finite length expression constructed from variables (also known as indeterminates) and constants, by using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents."
and for something like
that dosent work cause cos is not a real number?
That works, but as a trigonometric function and not a polynomial function. I the definition of a polynomial function, the right hand side must be a polynomial, as defined above.
Thank you :D