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Polynomials or not?

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Solution

Solution by Ancient Tree · EN

$P$ 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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