Polynomials or not?

Are the following functions polynomials in $x$ ?

$P(x)=2x+1,\quad Q(x)=18x^{2}+\frac{2}{x},\quad R(x)=x^{3}+x^{2}+\sqrt{x}, \quad f(x)=15x^{5}+16x^{2}.$

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$P$ is a polynomial (of degree $1$ ).
$Q$ is not a polynomial, because it involves a fraction where the denominator is a polynomial, which cannot be simplified to something like $x^{k}$ . By the way, $Q$ is called a rational function.
$R$ is not a polynomial, because it involves a square root.
$f$ is a polynomial (of degree $5$ ).

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