Vector Space: Fifth-Degree Polynomials

[eyehategod]

15. Determine wheter the set is a vector space.
The set of all fifth-degree polynomials with the standard operations.
AXIOMS
1.u+v is in V
2.u+v=v+u
3.u+(v+w)=(u+v)+w
4.u+0=u
5.u+(-u)=0
6. cu is in V
7.c(u+v)=cu+cv
8.(c+d)u=cu+cd
9.c(du)=(cd)u
10.1(u)=u

the axioms that fail are 1,4,5, and 6. I don't know why 4,5,and 6 fail. Can anyone help me?

 

[Gokul43201]

How is the degree of a polynomial defined? Now, what is the additive identity, and is it a fifth-degree polynomial?