How would I approach this problem??

Determine whether the following are vector spaces:
1) The set of real polynomials of x divisible by x^2+x+1;
2)The set of differentiable functions of x on [0,1], whose derivative is 3x^2.

Question

How would I approach this problem??

Determine whether the following are vector spaces:
1) The set of real polynomials of x divisible by x^2+x+1;
2)The set of differentiable functions of x on [0,1], whose derivative is 3x^2.

anonymous · Answer

I think that a vector space is a space where the result of each linear combination of any number of vectors contained in the vector space, is contained in the vector space. That is if we call the vector space V:

If $$x_{1}, x_{2}, ... , x_{n} \in V$$
then
$$a_{1}x_{1}+a_{2}x_{2}+...+a_{n}x_{n} \in V$$

If I'm wrong, correct me please.

anonymous · Answer

Forgot to say that $$a_{1},a_{2},...,a_{n} \in \mathbb{R}$$

anonymous · Answer

Thanks, I'm still a bit lost but I'll get this. :)