# Is h(x) = sqrt{x} times (sqrt{x} - 1) a polynomial function and if so what is the degree?

$h \left(x\right) = \sqrt{x} \times \left(\sqrt{x} - 1\right) = x - \sqrt{x}$
In a polynomial only expressions like ${x}^{n}$ for natural $n$ are allowed. $h \left(x\right)$ contains $\sqrt{x}$ so it is not a polynomial.