The Puzzling Case of Positive Polynomials: A Vector Space?

[Workout]

Homework Statement

Is the set of all polynomials with positive coefficients a vector space?

It's not.

But after going through the vector space conditions I don't see how it can't be.

 

[jedishrfu]

what are the inverse elements of the space?

 

[mfb]

But after going through the vector space conditions I don't see how it can't be.

If you show your work, it is easier to find your error.
Oh, and you have to specify the field for the vector space (probably R).

Edit: Or use the direct hint given above ;).

 

[HallsofIvy]

One of the properties that a vector space must have is that it is "closed under scalar multiplication". That is, the product of any real number a, and vector v, av is also a number. v= x+ 1 is a "polynomial with positive coefficients" and a= -1 is a number. What is av?