1. The problem statement, all variables and given/known data The problem asks, find a basis for the P2 subspace that consists of polynomials, p(x) such that p'(5)=0. 3. The attempt at a solution I know that a set of vectors is a basis if it's linear independent and spans the vector space. So I let p(x) = ax2 + bx +c . Then p'(x) = 2ax + b. p'(2) = 4a + b I set that equal to 0. so 4a+b = 0. then 4a=-b, and a= =1/4*b. Now I am stuck as to where to go from here when finding a basis (prof hasn't really taught this yet) I was wondering what the next step would be? Thank you.