Let C[1; 1] be the vector space of all continuous functions over the interval 1 x 1. Let (f; g) be the inner product on C[1; 1] given by (f; g) = Z 1 1 f(x)g(x) dx: Find the cubic polynomial x3 + ax2 + bx + c that is orthogonal to 1; x and x2 1 3 in C[1; 1] under the inner product (f; g) dened above.

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