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).
