Dimension of subspace of even and odd polynomials

[charmmy]

Homework Statement

I have a question which asks me to find the dimensions of the subspace of even polynomials (i.e. polynomials with even exponents) and odd polynomials.

I know that dim of Pn (polynomials with n degrees) is n+1. But how do I find the dimensions of even n odd polynomials?

Homework Equations

The Attempt at a Solution

 

[fzero]

You might want to consider a few examples until you can guess what happens in the general case. The answer will depend on whether n is even or odd.