A polynomial is an expression where the exponents of the variables are non-negative integers.

A polynomial is an expression where the exponents of the variables are non-negative integers.
The given expression is $f(x) = \frac{3}{x^2} + x$.
The term $\frac{3}{x^2}$ can be rewritten as $3x^{-2}$.
In this term, the exponent of $x$ is $-2$, which is a negative integer.
Since a polynomial requires all variable exponents to be non-negative integers, $f(x)$ is not a polynomial.