1. The problem statement, all variables and given/known data Let Pn denote the linear space of all real polynomials of degree </= n, where n is fixed. Let S denote the set of all polynomials f in Pn satisfying the condition given. Determine whether or not S is a subspace of Pn. If S is a subspace, compute dim S. The given condition if f(0)=f(1) 2. Relevant equations Closure axioms: (1)Closure under addition: For every pair of elements x and y in V there corresponds a unique element in V called the sum of x and y denoted by x+y. (2) Closure under multiplication: For every x and y in V and every real number a there corresponds an element in V called the product of a and x, denoted by ax. 3. The attempt at a solution I know that S is a subspace of Pn if S is a subset of Pn and it satisfies the closure axioms. So I need to prove these three things, but they seem trivial to me. S c Pn because S: f(0)=f(1) has all elements in Pn. Is this enough of a proof to draw the conclusion? For the closure axioms, I know that I have to show that f(x)+g(x) is an element in Pn, but again this seems trivial, I am unsure how to do this. Same for the closure axiom of multiplication.