1. The problem statement, all variables and given/known data Let P denote the set of all polynomials whose degree is exactly 2. Is P a vector space? Justify your answer. 2. Relevant equations (the numbers next to the a's are substripts P is defined as ---->A(0)+A(1)x+A(2)x^2 3. The attempt at a solution I really dont know how to do this problem. i want to say that it isn't a vector space because it violates the property of having an additive inverse. as in, there is no value of x such that F(x) + (F(-x)) = F(x)+(-F(x)) = 0 if we keep all of the values for A the same A(0) + A(1)x + A(2)x^2 + A(0) + A(1)(-x) + A(2)(-x)^2 == 2A(0) + 2A(2)x^2 != 0 therefore, there is no additive inverse. i probably did it wrong, but i dont know. all i know is that the book says that it isnt a vector space, but it doesnt give the reason.