\alpha p_1(x) + \beta p_2(x) = \frac{-(\alpha c_1 + \beta c_2) + (\alpha d_1 + \beta d_2)}{2}x^3 + \frac{3 (\alpha c_1 + \beta c_2) + (\alpha d_1 + \beta d_2)}{2}x^2+(\alpha c_1 + \beta c_2)x+(\alpha d_1 + \beta d_2)