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/
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