Determine if the expression: $\frac{5x^{3}y}{x}$ is a polynomial. Show your reasoning.

No; because dividing by the variables always produces non-polynomial expressions, regardless of simplification

No; because dividing by $x$ results in a negative exponent when rewritten using exponent rules, so it is not a polynomial

Yes; because the numerator has only whole-number exponents, and the presence of division does not matter

Yes; it simplifies to: $5x^{2}y$, which is a monomial and therefore is a polynomial