Which of the following are not polynomials?

First, ask yourself:  What is a polynomial?  It's an algebraic expression in which all powers of x are zero or positive integers.
Eliminate E because -2 is not a positive integer exponent.
Accept D because all of the powers of x are positive integers:  {3, 2, 1, 0}
Eliminate C because -3 is not a positive integer power
Eliminate A and B because of the fractional or negative exponents shown.

Only D is a polynomial.