Which statement correctly expresses the defining property of a polynomial?

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

Simplify the expression $E\left(x\right)=\frac{x^3-2}{x}$ and determine if it is a polynomial.

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

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