Is 18 a Polynomial? Understanding Polynomials and Degrees

[Hawksteinman]

Homework Statement

Is the following a polynomial or not: 18

Homework Equations

The Attempt at a Solution

Not a polynomial (computer says it is)

 

[DrClaude]

What is the definition of a polynomial?

And what is that computer that's giving you answers?

 

[Hawksteinman]

What is the definition of a polynomial?

And what is that computer that's giving you answers?

A polynomial is of the form ax^n + bx^m where a, b, n, and m are integers

And it's a test on mymathlab.com that counts 2.5% to my final grade (I get unlimited tries until October 26th)

 

[DrClaude]

A polynomial is of the form ax^n + bx^m where a, b, n, and m are integers

That's not a very good definition (and false if one is to take a and b as integers only). Have a look at Wikipedia for a better one.

But even with your definition, can you find coefficients a, b, n, and m such that the result is ax^n + bx^m = 18?

 

[Hawksteinman]

That's not a very good definition (and false if one is to take a and b as integers only). Have a look at Wikipedia for a better one.

But even with your definition, can you find coefficients a, b, n, and m such that the result is ax^n + bx^m = 18?

Thanks :D

Yes, but 18 itself isn't a polynomial?

 

[Hawksteinman]

Or is 18 just a polynomial of order 0

 

[DrClaude]

Yes, but 18 itself isn't a polynomial?

Or is 18 just a polynomial of order 0

In general parlance, no, 18 is not a polynomial. But in the context of polynomials, you can indeed say that 18 is a polynomial of degree 0, with only a constant coefficient.