Which of the following expressions best matches the definition of a polynomial?

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

Is $\sqrt{x}+x^2$ a polynomial? Use exponent rules to justify your answer.

A rectangular plot has length $L=x+2$ and width $W=x-3$. Form the polynomial expression for the area and determine its degree.

Determine the degree of the polynomial $P(x,y)=x^4+2x^2{y}^3+y^6$ and justify how you found it.