W is the set of all polynomials in P_2 such that p(1)=0 is a subspace of P_2. Find a basis for W...I know that the answer is (t-1,t^2-1). This is correct because any coordinates chosen relative to the basis vectors remains in the subspace of p(1)=0. Fore example, 5(t-1)+2(t^2-1)= 2t^2+5t-7.....p(1)=2(1)+5(1)-7....p(1)=0....I just want to know how to discover this basis so that I can solve similar problems in the future.

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