# Types of polynomial functions. Quadratic, cubic, quartic, quintic, …,?

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 en.wikipedia.org/wiki/Number_prefix there under "ordinal" –  Alex Youcis Oct 28 '11 at 0:55
@Alex: You could write this as an answer so it can be accepted and the question doesn't remain unanswered. –  joriki Oct 28 '11 at 1:04
Joiki, thank you for the advice. I will do that. –  Alex Youcis Oct 28 '11 at 1:05
There’s something just a little ... unsavory ... about the expression septic equation. –  Brian M. Scott Oct 28 '11 at 1:25
@Brian: By all means, don't try to eat a polynomial. –  The Chaz 2.0 Oct 28 '11 at 1:28

## 2 Answers

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 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 does mention heptimic and septimic...) –  ShreevatsaR Oct 28 '11 at 3:04
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... –  Steven Stadnicki Oct 28 '11 at 3:52
I agree. Searching for "octavic" brings up this book ("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 has 280 results and octic 2060; sextic septimic 74 and [sextic septic] 241. –  ShreevatsaR Oct 28 '11 at 4:06
Now looking back, I do recal a vague memory of it saying septimic in my Algebra book. –  HaydenStudios Oct 28 '11 at 17:50
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 –  AndyP Nov 11 '14 at 4:55

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".

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