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
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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