Let p₀, p₁, and p₂ be the orthogonal polynomials described in Example 5, where the inner product on P⁴ is given by eval-uation at -2, -1, 0, 1, and 2. Find the orthogonal projection of t³ onto Span {p₀, p₁, p₂}.

Data From Example 5

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EXAMPLE 5 Let V be P4 with the inner product in Example 2, involving evaluation of polynomials at -2, -1, 0, 1, and 2, and view P₂ as a subspace of V. Produce an orthogonal basis for P₂ by applying the Gram-Schmidt process to the polynomials 1, t, and 1².