Question

Check whether $x^2+3x+5$ and $x+\sqrt{x}-3$ are a polynomials or not?

Answer 1

$\text{All the variables of a polynomial}\text{should have whole numbers as}\text{exponents.}$
In polynomial $x^2+3x+5$ 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 $x+\sqrt{x}-3$, 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 $x^2+3x+5$ is a polynomial.