Can a polynomial ever just have 2 terms?

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    Polynomial Terms
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Discussion Overview

The discussion revolves around the definition and characteristics of polynomials, specifically addressing whether a polynomial can consist of only two terms. Participants explore the structure of polynomials, including their terminology and the operations allowed within them.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that a polynomial must have at least three terms to be considered a polynomial.
  • Others argue that a polynomial can consist of one term (monomial), two terms (binomial), or three terms (trinomial), and provide definitions for these terms.
  • There is a discussion about whether division is permissible in polynomials, with some stating that expressions involving division do not qualify as polynomials, while others contend that division can be viewed as multiplication by a constant.
  • Participants mention specific examples of polynomials, such as $x^2 - 4$ as a valid polynomial with two terms.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether a polynomial can have only two terms, as some assert it can while others maintain it cannot. The discussion remains unresolved regarding the inclusion of division in polynomial expressions.

Contextual Notes

Some definitions and terminology regarding polynomials are presented, but there are differing interpretations of what constitutes a polynomial based on the number of terms and the operations involved.

OMGMathPLS
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Or does it always have to have MORE THAN 2 like

x^2 +x^2 -4a polynomial can never be

x^2 - x-^3

Right?
 
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i don't fully understand your question but yes there can be x^2 and x^3 and x^4 and x^5 etc...
 
Whoops. Sorry I mean

A polynomial can never be

term +/-/*/divide term (only 2 terms)

it must be

term term term

at least 3 right? To be considered a polynomial?
 
In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

A polynomial can have as few as 1 term, which is a monomial. Two terms and the polynomial can also be called a binomial, and 3 terms is a trinomial. I tend to use the special names for smaller polynomials though. Also, polynomials in one variable have special names related to the order. Instead of using trinomial, I would call $x^2+x+1$ a quadratic, meaning it is a second order polynomial, because the largest exponent is 2.

With regard to order, there are constant, linear, quadratic, cubic, quartic, quintic, etc. polynomials.
 
well you can have something like $x^2-4$ which is only two terms and a polynomial CAN include division like $x^2/2...$
 
Oh ok. Thanks.

The Issac Newton picture fits you.
 
lol mark is isaac Newton.
 
ineedhelpnow said:
...a polynomial CAN include division like $x^2/2...$

Good point, but we could also view this as multiplication by 1/2. I think the restriction of not allowing division would be as in the following example:

$$\frac{x^2+x+1}{7x+2}$$

is not a polynomial, whereas,

$$\left(x^2+x+1\right)(7x+2)$$

is a polynomial, written in factored form.
 
OMGMathPLS said:
Oh ok. Thanks.

The Issac Newton picture fits you.

Hey, I never noticed that, but Geddy Lee does bear a certain resemblance to Newton. (Smirk)
 
  • #10
Lol
 
  • #11
OMGMathPLS said:
Lol

Just so you know for the future, we try to discourage the use of "textspeak" abbreviations, simply because we want to appeal to as wide a global audience as possible, and many folks around the world may not be familiar with these abbreviations and would be left wondering what it means. :D
 
  • #12
MarkFL said:
Hey, I never noticed that, but Geddy Lee does bear a certain resemblance to Newton. (Smirk)
Soooooo... Can we drop apples on him?

-Dan
 

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