MHB Is This Function a Polynomial?

[karush]

$2x^{-3}-2x^{2}+3$

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?

 

[Nono713]

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" :)

 

[Jameson]

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.

 

[karush]

this is a overleaf project I am working lots of pre calc problems
140 pdf 100 pages