Let P be the vector space consisting of all polynomials with degree less than or equal to 2, where the field that P is over is the set of rationals. Now let E2 be the subspace of all stuff in P that has a root of 2, let E5 be the subspace of all elements in P that have a root of 5. Show that P=E2+E5, where + is the subspace sum.
This isn't a homework problem, but it's a problem that I've been having difficulty with, so any help would be much appreciated. Thanks