Why can’t polynomials have negative exponents?

Question

Polynomials cannot have a variable as a demonenator because that would mean it has a negative exponent. My question is why it cannot have a negative exponent. The simplest answer would be appreciated 

Answer 1

By DEFINITION, a polynomial of degree n is an expression of the form

 

a₀ + a₁x + a₂x² + ... + a_nxⁿ

 

where

 

n > 0

 

and

 

a_n ≠ 0.  There is no "why" to it; it is a definition.  

Answer 2

Because then it would have the variable in the denominator.

 

Ex.   2x^-2 + 3x + 4 = 2/x^2 + 3x + 4 <--- not a polynomial