Oh right, silly me. Wow, my own vocabulary deserted me there, huh?
Yeah I think generally "sextic" is the highest you see before people stop doing that, and that one's somewhat uncommon I'd say. ("Quintic" is actually fairly common, contrary to what I said earlier, oops.) The fact that seventh-degree would be "septic" might be one reason stop with the words at that point!
I'm pretty sure that more than half the times I've seen "quintic" are in one single context: talking about the fact that while you can solve polynomial equations of degree 1-4 by doing arithmetic and taking n'th roots, this stops being possible once you get as far as quintic equations. (The "insolubility of the quintic".)
Yeah I think generally "sextic" is the highest you see before people stop doing that, and that one's somewhat uncommon I'd say. ("Quintic" is actually fairly common, contrary to what I said earlier, oops.) The fact that seventh-degree would be "septic" might be one reason stop with the words at that point!