MHB Is This Function a Polynomial?

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The function $2x^{-3}-2x^{2}+3$ is not a polynomial because it contains a term with a negative exponent, which violates the definition of polynomials requiring non-negative integer exponents. Polynomials must be continuous and differentiable everywhere, lacking asymptotes, which this function has due to the negative power. The highest degree term in the expression is $-2x^2$, indicating a degree of 2, but this does not classify it as a polynomial. The leading coefficient is 2, but the presence of the negative exponent disqualifies the function from being a polynomial. Therefore, the function does not meet the criteria to be classified as a polynomial.
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$2x^{-3}-2x^{2}+3$

Decide whether the function is a polynomial function, If so, states its degree, type, and leading coefficient.

well, I presume it is a polynomial since it the sum of powers in the variable x. Its degree is 2 since that is highest power, but I don't know its type, since it is not quadratic or cubic. and has a vertical asymptote. and of course the leading coefficient is 2

couldn't find the answer in the book?
 
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Polynomials cannot have negative powers of $x$, so it's not a polynomial. Polynomials are continuous everywhere, differentiable everywhere, are well-behaved and have no asymptotes.

See the Wikipedia article, it says "non-negative integer exponents" :)
 
One of the criteria for an expression to be a polynomial is that the exponents must be non-negative integers. So given that piece of information, what do you say the answer is?

Here's a site that goes over some examples.
 
this is a overleaf project I am working lots of pre calc problems
140 pdf 100 pages
 

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