Question

Let p₁ (t) = 2t² +t + 2, P₂ (t) = t² - 2t, p₃(t) = 5t²-5t+2, p₄(t)=-t²-3t-2 in P₂. Determine whether the vector p(t)= t²+t+2 belongs to span{p₁(t), p₂(t), P₃(t), P₄(t)).