Let f_1 = -3 + 2x + 2x^2, f_2 = 5 + x^2, f_3 = -20 + 8x + 7x^2 and f_4 = 3. give the definition of span{f_1, f_2}. use definition to show that h = span{f_1, f_2} is a subspace of p_2(x). find a basis of h. is f_3 in h? find a basis of p_2(x) containing {f_1, f_2}. is {f_1, f_2, f_3, f_4} a basis of p_2(x)? give a brief explanation for your answer. let b = {f_1, f_2, f_3}. find [f_4]b. let c = {f_4, f_5 = 3f_1 + 2f_2, f_6 = 2f_1 - 3f_2}. find p_c leftarrow b.