Hi. Thanks for the help. 1. The problem statement, all variables and given/known data Find a basis for the set of polynomials in P3 with P'(1)=0 and P''(2)=0. 2. Relevant equations P' is the first derivative, P'' is the second derivative. 3. The attempt at a solution The general form of a polynomial in P3 is ax^3+bx^2+cx+d Therefore, P' will have the form 3ax^2+2bx+c and P'' will have the form 6ax + 2b Plugging in the known values, the two equations will be: 3a+2b+c=0 12a+2b+0c=0 I just don't know where to go from there, how to find the basis. I understand the concept of a basis and how to find one for a set of matrices or vectors, but not with this. Any help would be greatly appreciated. Thank you.