So I'm kind of running into a wall with this one. It should have pretty simple solutions but I'm just not seeing it.
Let X be the the set of all polynomials with degree less than or equal to n. X is a vector space. A polynomial p e X has the form:
Are the following sets subspaces of X for all x e R?
For W1 I've shown that:
So it must be a subspace. But I'm not sure how to proceed with W2 and W3. Intuition tells me W2 is a subspace too, but I'm not sure how to show that mathematically. Any tips?
is a subspace .