Let p₀, p₁, p₂ be the orthogonal polynomials described below, where the inner product on P₄ is given by evaluation at -2, -1, 0, 1, and 2. Find the orthogonal projection of 2t³ onto Span{p₀, p₁, p₂}.
p₀(t) = 1
p₁(t) = 4t
p₂(t) = t² - 2.
Question content area bottom Part 1:
The orthogonal projection of 2t³ onto Span{p₀, p₁, p₂} is enter your response here. (Simplify your answer.)