Question

Are they both polynomials ?​

Answer 1

No, they are not polynomials.

Criteria to become a polynomial: the powers or exponents of variables should be whole numbers, (0, 1, 2, 3, ..., ∞).

For $7x^3 - \frac{3}{x^2} + \sqrt{5}$, the exponent of $x$ in the expression $- \frac{3}{x^2} = 3x^{-2}$ is not a whole number. Thus, it is not a polynomial.

For $2x^2 y - \frac{3}{xy} + 5 y^3 + \sqrt{3}$, the exponent of $xy$ in the expression $- \frac{3}{xy}$ is not a whole number.

∴ None of these are polynomials.