A polynomial is a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied with one or more variables raised to a non-negative integral power . For example, $(a+bx+c{x}^2)$ where a, b and c are constants, and x is the variable.

Degree is the highest power of the variable.
$4x+2$ is a polynomial of degree 1.

$\frac{1}{(x+1)}=(x+1{)}^{-1}$, the degree of this expression would not be non-negative. Thus, it is not a polynomial.

$4x+2=0$ is an equation and hence not a polynomial.

$x+y$ is a polynomial in two variables, x and y.