Nomial

So I try another dictionary!  Webster's New World Dictionary 
says: "[POLY- + [BI)NOMIAL]", which sends me to look up the word 
binomial.  This says, indeed, "[< LL binomius < bi- + Gr. nomos, law 
+ -AL]".  It is defined as "a mathematical expression consisting of 
two terms connected by a plus or minus sign."  Hmm... maybe each term 
was considered to be a "law" or rule, and a binomial tells you to 
follow both rules, then add the results together.

I know one good Web source that may be able to clear up the matter:

  Earliest uses of mathematical words
    http://jeff560.tripod.com/mathword.html 

Let's look up "polynomial" and "binomial" there.  Maybe it will help. 
Here is what I find:

POLYNOMIAL was used by Fran�ois Vi�ta (1540-1603) (Cajori 1919, page 
139). 

The word is found in English in 1674 in Arithmetic by Samuel Jeake 
(1623-1690): "Those knit together by both Signs are called...by some 
Multinomials, or Polynomials, that is, many named" (OED2). 
[According to An Etymological Dictionary of the English Language 
(1879-1882), by Rev. Walter Skeat, polynomial is "an ill-formed 
word, due to the use of binomial. It should rather have been 
polynominal, and even then would be a hybrid word."] 

That confuses things, rather than clearing up the matter!  When it 
says "many named", it is implying (I think) that the -nomial part 
comes from the Latin word nomen, "name", rather than from Greek 
nomos, "law".  The same is suggested by the critique of the word as 
ill-formed and hybrid, that is, a mix of Greek and Latin.

So it looks like there is confusion about where the -nomial part comes 
from, because the word polynomial was created in a messy manner--like 
many new words today that are just formed by sticking two words 
together, or taking parts of words, without considering where those 
words came from.  The New World Dictionary and the Skeat quote above 
both suggest that "polynomial" was formed on the pattern of 
"binomial", rather than being constructed directly from Greek (or 
Latin) roots; and "binomial" itself appears to be a hybrid Latin-
Greek word.

The best answer to your question may be that -nomial may derive from 
Greek nomos, "law", influenced by Latin nomen, "name", or perhaps 
the other way around, but we don't know for sure.