For an expression to be a polynomial, exponents of variables must be a natural number (1, 2, 3, etc.) or 0. So exponents on variables cannot have negative exponents or roots (as roots are fraction exponents). As the third answer choice, 5x^2 - sqrt(x), contains the square root of a variable ( sqrt(x) is also equal to x^(1/2) ), it is not a polynomial.
