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July 29, 2015

Posted by **Lena** on Tuesday, September 8, 2009 at 9:48pm.

I was thinking that this was not a polynomial function because -7x is just one term making it a monomial but the answer key says it is a polynomial function. Could someone explain why that is so? Thanks :D

- Math:Polynomial Functions -
**MathMate**, Tuesday, September 8, 2009 at 10:07pmYou have a point, but the definitions are that

a monomial has only one term,

a binomial has exactly two terms,

a trinomial has exactly three terms, and

a polynomial has*at least*one term.

Ususally polynomial is used when the number of terms is numerous, unknown or indefinite. It would be too restrictive if 1-3 terms are excluded from the definition.

- Math:Polynomial Functions -
**Lena**, Tuesday, September 8, 2009 at 10:14pmwhy would something like y=x^-3 not be a polynomial function?

- Math:Polynomial Functions -
**Lena**, Tuesday, September 8, 2009 at 10:16pmmust the value of n always be nonnegetive?

- Math:Polynomial Functions -
**MathMate**, Tuesday, September 8, 2009 at 10:25pmYes, the exponents have to be non-negative (i.e. zero allowed, thus constant terms) and integers. x

^{2/3}and x^{-2}are not polynomials.

The definition of a polynomial, as per Wiki, is as follows:

"In mathematics, a polynomial is a finite length expression constructed from variables (also known as indeterminates) and constants, by using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents."

- Math:Polynomial Functions -
**Lena**, Tuesday, September 8, 2009 at 10:28pmand for something like

y=cosx

that dosent work cause cos is not a real number?

- Math:Polynomial Functions -
**MathMate**, Tuesday, September 8, 2009 at 10:50pmThat works, but as a trigonometric function and not a polynomial function. I the definition of a polynomial function, the right hand side must be a polynomial, as defined above.

- Math:Polynomial Functions -
**Lena**, Tuesday, September 8, 2009 at 10:57pmThank you :D

- Math:Polynomial Functions -
**MathMate**, Tuesday, September 8, 2009 at 11:12pmYou're welcomd!