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### Names of Polynomials

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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?
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```
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)

"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

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/
```
Associated Topics:
High School Definitions
High School Polynomials
Middle School Definitions

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