Names of Polynomials

Date: 11/25/97 at 17:25:55
From: Chris Elbert
Subject: Names of polynomials

Every year, I discuss classification of polynomials by their degree 
and give names for each class. However, I am only aware of the names 
for up to degree 5. Are polynomials with higher degree named, and, 
if so, what are they called?

Date: 12/01/97 at 12:35:18
From: Doctor Mark
Subject: Re: Names of polynomials

Hi Chris,

Well, yes, they do have names, but they are sometimes not terribly
standard.  We have

degree   name

   1     linear (or monic)

   2     quadratic (a little confusing, since "quad" usually means 
         "4"; the 'quad comes from the fact that the area of a square 
         of side x is x^2, and a square has 4 sides)

   3     cubic

   4     quartic (in older algebra books, it  is also called a 
         "bi-quadratic" polynomial)

   5     quintic

   6     this one might get you in trouble with the principal/parents, 
         but the kids will like it: "sextic" (or, the less troublesome 
        "hexic," which might get you in trouble around Hallowe'en)

   7     my personal favorite:  "septic" (as in system) or "heptic"

   8     octic

   9     nonic (almost sounds like it's a "non-equation")

  10     decic (which sounds as if you have something stuck in your 
         throat)

I have seen the names up to 8 in print, but not the names for 9 and 
10: one normally just says "a ninth degree polynomial."

There's also a name for a polynomial of 100th degree which is also a 
little amusing:  "hectic."  Which is probably how you would feel if 
you had to write it down under time pressure.

I'm assuming you also know that there is a formula for the solution of
equations of degrees 2, 3, and 4,  but not for 5 and above.  That is, 
there is a "cubic formula" and a "quartic" formula, but no such thing 
as a "quintic" or "septic" formula. If you ever saw the cubic or 
quartic formulas, you would understand why no one ever told you about 
them: they're pretty unpleasant little things (but, of course, pretty 
in their own right).

-Doctor Mark,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/