Question

For an expression to be a polynomial what must be true about the exponents of the variables?

Answer 1

The exponents must be non-negative integers.

Examples:

$x$ is a polynomial (degree 1)

$x^2-1$ is a polynomial (degree 2)

$x^3-\dfrac1{x^3}=x^3-x^{-3}$ is NOT a polynomial, but a rational expression

$\sqrt x=x^{1/2}$ is NOT a polynomial, but an algebraic expression.