Answer
Not a polynomial, because not all terms in the sum are monomials.
(The variable has a negative exponent in one of the terms)
Work Step by Step
A monomial is an expression of the form $ax^{k}$,
where $x$ is the variable,
the exponent $k$, a nonnegative integer, is the degree,
and $a$ is the coefficient of the term.
A polynomial expression is either a single monomial or a SUM of several monomials.
The degree of the polynomial is the degree of the monomial with the highest degree.
Here, we have
$3x^{2}-\displaystyle \frac{5}{x}=3x^{2}-5x^{-1}$
The second term is not a monomial, because the variable has a negative exponent.
So, the expression is not a polynomial.
Not a polynomial, because not all terms in the sum are monomials.
(The variable has a negative exponent in one of the terms).
