MHB Can a polynomial ever just have 2 terms?

[OMGMathPLS]

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?

 

[ineedhelpnow]

i don't fully understand your question but yes there can be x^2 and x^3 and x^4 and x^5 etc...

 

[OMGMathPLS]

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?

 

[MarkFL]

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.

 

[ineedhelpnow]

well you can have something like $x^2-4$ which is only two terms and a polynomial CAN include division like $x^2/2...$

 

[OMGMathPLS]

Oh ok. Thanks.

The Issac Newton picture fits you.

 

[ineedhelpnow]

lol mark is isaac Newton.

 

[MarkFL]

...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.

 

[MarkFL]

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)

 

[OMGMathPLS]

Lol

 

[MarkFL]

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

 

[topsquark]

Hey, I never noticed that, but Geddy Lee does bear a certain resemblance to Newton. (Smirk)

Soooooo... Can we drop apples on him?

-Dan