If this is meant to be x^2+4x^(3/2) then it isn't a polynomial, because we have a non-integer power of the variable. Polynomials have integer powers by definition, and the integers must be positive.
If it's meant to be x^2+(4x^3)/2 then it is a polynomial, but then you would have to ask why it isn't shown as x^2+2x^3.