Let S denote the collection of all polynomials of the form p(t) = (2a - b)t^2 + 3(c - b)t + (a - c), where a,b,c are real numbers. Determine whether or not S is a subspace of P2.
The Attempt at a Solution
Okay, so I know that in order for S to be a subspace, it must satisfy 3 conditions
1. closure of addition
2. closure of scalar multiplication
3. the set is not empty
I don't know how to show that S is a subspace of P2, my textbook does not give good examples. What should I do first?