Given two subspaces of the vector space of all polynomials of at most degree 3 what is the general method to calculate the intersection of the two subspaces?
What is the general method to calculate the intersection of two subspaces of any vector space? It's not even clear what you mean when you say the word "calculate" - are you looking for a basis? If you have a specific problem or example in mind it would be a lot easier if you tell us what it is.