Prove that this set is a vector space (by proving that it is a subspace of a known vector space). The set of all polynomials p with p(2) = p(3).
I understand I need to satisfy, vector addition, scalar multiplication and show that it is non empty.
I'm new to this concept so not even sure how to start. Do i maybe use P(2)-P(3)=0 instead?
My concern is I'm not sure what two polynomials I need to add to prove vector addition; proving scalar multiplication seems okay though.
Thankyou also a follow up question; if I prove something is a subspace of a known vector space does this imply the subspace is a vector space. Or does that subspace has to span the entire vector space first? how would i prove this in this case?