# Algebra question: Names of polynomial components? **URL:** \ **Category:** Factual Questions\ **Created:** [November 14, 2011, 7:27pm UTC](https://boards.straightdope.com/t/algebra-question-names-of-polynomial-components/602926 "2011-11-14T19:27:46Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![Earl\_Snake-Hips\_Tucker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/earl_snake-hips_tucker/32/3269_2.png) [@Earl\_Snake-Hips\_Tucker](https://boards.straightdope.com/u/Earl_Snake-Hips_Tucker)\ **Post date:** [November 14, 2011, 7:27pm UTC](https://boards.straightdope.com/t/algebra-question-names-of-polynomial-components/602926/1 "2011-11-14T19:27:46Z")
I’m pretty sure I never learned this term, if there is one. Anyway. . . For example: X[sup]2[/sup] + x + 1 = 0 The “x squared” component is called the. . . what? Is there a name for the squared, cubed, (and higher powers) components (other than, in this case, the “squared component)? ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [November 14, 2011, 7:45pm UTC](https://boards.straightdope.com/t/algebra-question-names-of-polynomial-components/602926/2 "2011-11-14T19:45:22Z")
The names I’ve usually heard are: [ul][_]x[sup]2[/sup]: Quadratic[_]x[sup]3[/sup]: Cubic[_]x[sup]4[/sup]: Quartic[_]x[sup]5[/sup]: Quintic[/ul]Beyond this, I’ve not heard any names in common usage, though that doesn’t mean they don’t exist. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [November 14, 2011, 7:49pm UTC](https://boards.straightdope.com/t/algebra-question-names-of-polynomial-components/602926/3 "2011-11-14T19:49:14Z")
> [@Earl\_Snake-Hips\_Tucker](#): > > The “x squared” component is called the. . . what? Is there a name for the squared, cubed, (and higher powers) components (other than, in this case, the “squared component)? Can’t go wrong with “the second-order term”. I’ve been rarely known to refer to x[SUP]4[/SUP] as “x tesarracted”, but only when I’m being a twit. ---
**Author:** ![John\_Mace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_mace/32/185_2.png) [@John\_Mace](https://boards.straightdope.com/u/John_Mace)\ **Post date:** [November 14, 2011, 7:50pm UTC](https://boards.straightdope.com/t/algebra-question-names-of-polynomial-components/602926/4 "2011-11-14T19:50:32Z")
Also, I would call the example in the OP a “2nd order polynomial”. Often, polynomials are used to approximate a function (by expanding that function out as an infinite series). If we were to truncate it to: a +bx, then that would be the “first order approximation”, since we only took it out to one power of x. That is what mathematicians and scientist mean when they use that term (1st, 2nd etc order approximation). Sometimes they will used “first order” to mean just an approximation, if they are talking in the vernacular, but if they are being rigorous about things (like in a paper, or a talk to other scientists), they will mean the order of the polynomial expansion they are assuming in their model. ---
**Author:** ![robert\_columbia](https://avatars.discourse-cdn.com/v4/letter/r/e79b87/32.png) [@robert\_columbia](https://boards.straightdope.com/u/robert_columbia)\ **Post date:** [November 14, 2011, 7:58pm UTC](https://boards.straightdope.com/t/algebra-question-names-of-polynomial-components/602926/5 "2011-11-14T19:58:27Z")
It’s the “quadratic” term. A cubed component is the “cubic” term. Your example equation is known in high schools in the US as a “quadratic equation”. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [November 14, 2011, 8:00pm UTC](https://boards.straightdope.com/t/algebra-question-names-of-polynomial-components/602926/6 "2011-11-14T20:00:34Z")
x[sup]3[/sup] = cubic term x[sup]2[/sup] = quadratic term x = linear term. Beyond cubic, you could just call it an “nth-order term” where n is the exponent. ---
**Author:** ![Earl\_Snake-Hips\_Tucker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/earl_snake-hips_tucker/32/3269_2.png) [@Earl\_Snake-Hips\_Tucker](https://boards.straightdope.com/u/Earl_Snake-Hips_Tucker)\ **Post date:** [November 14, 2011, 8:03pm UTC](https://boards.straightdope.com/t/algebra-question-names-of-polynomial-components/602926/7 "2011-11-14T20:03:41Z")
OK, thanks all. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [November 15, 2011, 12:19am UTC](https://boards.straightdope.com/t/algebra-question-names-of-polynomial-components/602926/8 "2011-11-15T00:19:27Z")
To add on 2nd power = quardratic 3rd power = cubic 4th power = quartic or biquadratic 5th power = quintic But why doesn’t it go higher to sextic, septic, octic etc.? I think it is because a lot of the work in algebra in Western Europe a few centuries ago dealt with finding formulae that would give the roots of various degrees of polynomials using only field operators. The formulae for quadratic, cubic and quartic were found and so next in line was the quintic formula. Abel proved a general form for the quintic could not be found (which Galois improved upon) and so the naming of polynomials for higher degrees stopped.