Functions 1.1 + 3(x - 1) / 2.1 + 4(x - 1) + 10 * (x - 1) ^ 2 / 4 * on [- 1, 1] form the basis of the space of polynomials of degree 2 at most which is orthogonal with respect to the weight function w(x) = (1 + x) and associated inner product (f,g)w . For a given function x^5 , find the polynomial P(x) such that the error integral at w(x) * (x ^ 5 - P(x)) ^ 2 dx from -1 to 1 is minimized among all polynomial of degree 2