Question 4399
 For a given vector space V, a subset W is a subspace of V if and only
 if av+bw is in W for all v, w in W and scalars a,b.(reals here)
  
 Now W = {a + t^2| a is real} = set of polynomials in R with
 deg <=2 and the coefficient of t^2 = 1,  the coefficient of t = 0.
 Clearly, W is a subset of P2 = {a + bt + ct^2| a,b,c are reals} 
 = set of polynomials in R of degree <=2.

 But, W is not a subspace of P2.
 Since t^2 is in W but t^2 + t^2 = 2t^2 is not in W.  


 Kenny