1. The problem statement, all variables and given/known data Let F be a field. Prove that the set of polynomials having coefficients from F and degree less than n is a vector space over F of dimension n. 2. Relevant equations 3. The attempt at a solution Since the coefficients are from the field F, the are nonzero. So, if the polynomial has degree less than zero, its degree is at most n-1. Thus, the basis vector can be written a 1, u, ..., u^(n-1). Right? So then I should show that this basis vector is indeed a basis vector by showing that it spans and is linearly independent in order to conclude that the vector space has dimension n? I'm not sure how to go about that part.