Let f(x) be a polynomial of degree n in Pn(R). Prove that for any g(x) ∈ Pn(R) there exist scalars c0, c1, . . . , cn such that
g(x) = c0f(x) + c1f (x) + c2f’(x) + · · · + cnf” (n)(x), where f (n)(x) denotes the nth derivative of f(x).
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