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I would very much like to have a complete list of the types of polynomial functions. I know that theres:

Quadratic :                      (AX^2 + BX + C) Cubic     :               (AX^3 + BX^2 + CX + D) Quartic   :        (AX^4 + BX^3 + CX^2 + DX + E) Quintic   : (AX^5 + BX^4 + CX^3 + DX^2 + EX + F) 

What are the names of polynomial functions to the further powers? Sexstic? Septic? Octic? I'm not sure, so if someone could enlighten me, then that would be great. Please provide a list that goes at least to the seventh power, but it would be nice if you could go further. Thanks.

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    I think after quintic it becomes cumbersome to name them (since the prefixes become increasingly more complex). Thus, I feel like "degree seven" or "seventh degree" polynomial is more appropriate. If you are really interested in the prefixes look http://en.wikipedia.org/wiki/Number_prefix there under "ordinal"2011-10-28
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    @Alex: You could write this as an answer so it can be accepted and the question doesn't remain unanswered.2011-10-28
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    Joiki, thank you for the advice. I will do that.2011-10-28
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    There’s something just a little ... unsavory ... about the expression *septic equation*.2011-10-28
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    @Brian: By all means, don't try to eat a polynomial.2011-10-28
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    [Quite related...](http://math.stackexchange.com/questions/15899)2011-10-28
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    Polynomials have the interesting property that mathematicians need to be able to count beyond three to discuss some interesting properties they have. Imagine asking a similar question about 5-dimensional hyperplanes.2011-10-28
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    See the link below It explains the different Degrees http://en.wikipedia.org/wiki/Degree_of_a_polynomial2013-09-11

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While they do start getting awkward quickly, the next few ordinals are fairly well-defined, largely because of their occasional usage in solving cubic and quartic equations and in defining algebraic curves and surfaces: the Sextic, the Septic, and the Octic. Beyond that, they just don't show up often enough to be worth explicitly naming.

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    Strange... looking at http://en.wikipedia.org/wiki/Number_prefix under the "ordinal" column, it seems that the classically correct forms are actually **septimic** and **octavic**. (The WP link to [septic equation](http://en.wikipedia.org/wiki/Septic_equation) does mention *heptimic* and *septimic*...)2011-10-28
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    Those may be hypothetically correct, but I can safely say that I've never heard either of those - and have heard 'septic' and 'octic' repeatedly (not regularly, but often enough for them to stick in my head), and obviously (judging from Mathworld/etc) I'm not the only one. I like the sound of 'octavic', I have to admit, but it brings to mind music much more than mathemtics...2011-10-28
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    I agree. Searching for "octavic" brings up [this book](http://books.google.co.in/books?id=1Bmjde9vhLIC&pg=PA159&lpg=PA159&dq=octavic) ("the inscribed quartics hvae eight nodes on the octavic curve...") first published 1905, a paper from 1881, one from 1933, etc... all from an age when people were more likely to have been classically educated. :-) On Google Scholar, [octavic](http://scholar.google.com/scholar?q=octavic) has 280 results and [octic](http://scholar.google.com/scholar?q=octic) 2060; [sextic septimic](http://scholar.google.com/scholar?q=sextic+septimic) 74 and [sextic septic] 241.2011-10-28
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    Now looking back, I do recal a vague memory of it saying septimic in my Algebra book.2011-10-28
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    There's a list on Wikipedia pretty much reiterating what's been said here (along with mentioning the "proposed, but...rarely used" names **nonic** and **decic** for degrees 9 and 10.) [https://en.wikipedia.org/wiki/Degree_of_a_polynomial](https://en.wikipedia.org/wiki/Degree_of_a_polynomial)2014-11-11
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I think after quintic it becomes cumbersome to name them (since the prefixes become increasingly more complex). Thus, I feel like "degree seven" or "seventh degree" polynomial is more appropriate. If you are really interested in the prefixes look here under "ordinal".