To identify which expression is a polynomial, let's evaluate each option:

A. $\sqrt{13}$: This is a constant expression (since $\sqrt{13}$ is just a number), but polynomials cannot include square roots or fractional exponents of variables. Since $\sqrt{13}$ is not a polynomial expression.

B. $\frac{1}{x} + x$: This expression contains $\frac{1}{x}$, which is $x^{-1}$, a negative exponent. Polynomials cannot have negative exponents. Therefore, this is not a polynomial.

C. $x^{-2} - 3$: Here, $x^{-2}$ represents a negative exponent, and polynomials must have non-negative integer exponents. This is not a polynomial.

D. $\sqrt{x} + x$: $\sqrt{x}$ is the same as $x^{\frac{1}{2}}$, a fractional exponent, and polynomials do not allow fractional exponents. This is not a polynomial.

Conclusion: None of the expressions are polynomials, but the closest expression that might cause confusion is option A, which could be mistakenly thought of as a polynomial due to the constant $\sqrt{13}$. However, since no variables are involved, none of these are truly polynomials.

Would you like further details or have any questions?

Here are 5 related questions:

1. What are the key properties of polynomials?
2. Can a polynomial have negative exponents?
3. Why can't polynomials include fractional exponents?
4. How can you classify polynomials based on their degree?
5. What is the general form of a polynomial?

Tip: A polynomial consists of terms where the exponents of variables are non-negative integers.