1. The problem statement, all variables and given/known data 1) The set H of all polynomials p(x) = a+x^3, with a in R, is a subspace of the vector space P sub6 of all polynomials of degree at most 6. True or False? 2) The set H of all polynomials p(x) = a+bx^3, with a,b in R, is a subspace of the vector space P sub6 of all polynomials of degree at most 6. True or False? 2. Relevant equations Eh.. not sure? 3. The attempt at a solution Once more, not too sure. I've been pouring over my Linear Algebra book, but it seems so abstract... I was under the impression that as long as the polynomial didn't have a lower power than the vector space [number] that the polynomial would be in the subspace of the given vector space :\ Does the coefficient have anything to do with it? Some properties (if they help?): A subspace of a vector space V is a subset H of V that has 3 properties: a) The zero vector if V is in H. b) H closed under vector addition 3) H closed under scalar multiplication.. I've already gotten #1 wrong (the answer was false) - I'd like to know why though :( Any help would be awesome!