Use the subspace theorem to decide whether the following set is a real vector space with the usual operations. The set V of all real polynomials p of degree at most 2 satisfying p(1) = p(2), i.e. polynomials with the same values at x = 1 and x = 2.

Subspace Thereom:

-The set is non-empty

- A1 is satisfied (closure under addition)

- S1 is satisfied (closure under scalar multiplication)

Really stuck on this!! Thanks in advance for any help