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The following expressions in examples aren't polynomial expressions:

$2x^2-5x+(3/x)$ $9- \sqrt x$

Neither they are rational expressions, I've been just told that by book. but then what do you call them?

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    I'm not sure what the context is, but under many understandings the first one could be called rational.2011-10-09

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The two examples you gave are both algebraic functions, i.e. functions that satisfy a polynomial equation whose coefficients are rational functions. For example, $f=9-\sqrt{x}$ satisfies the polynomial equation $(y-9)^2-x=y^2-18y+(81-x)=0,$ i.e. $y=f$ is a root of this polynomial, and the coefficients of the polynomial are the rational functions $1$, $-18$, and $81-x$. However, as has been pointed out in the comments, $g=2x^2-5x+\tfrac{3}{x}$ is itself a rational function, so there is a particularly simple polynomial it satisfies (specifically, a linear polynomial) $y-(2x^2-5x+\tfrac{3}{x})=0.$

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    Of course, not all algebraic functions can be written as linear combinations of powers of $x$, as in the two examples given in the original post.2011-10-10
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I suppose you could call them Puiseux polynomials by analogy with Puiseux series, though I'm not sure anyone has ever done so.

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    @Mariano, sure, but then you could call polynomials "power series," and you'd be losing information if you did. By the way, I have found that the computer algebra program SAGE actually uses the term, "Puiseux polynomials," see http://trac.sagemath.org/sage_trac/ticket/92892011-10-10