All the variables of a polynomial should have whole numbers as exponents.
In polynomial x2+3x+5 the exponents of the variable x are 1 and 2. Here, 1 and 2 both are whole whole numbers. So, it is a polynomial.
In polynomial x+√x−3, the exponents of the variable x are 1, 1/2. Here 1/2 is not a whole whole number. So, it is not a polynomial.
Hence, only x2+3x+5 is a polynomial.