Let f(x) be a polynomial of degree n in Pn(R). Prove that for any g(x) in Pn(R) there exist scalars c0, c1, c2, ., cn such that g(x)=c0f(x)+ c1f'(x)+…

Let f(x) be a polynomial of degree n in Pn(R). Prove that for any g(x) in Pn(R) there exist scalars c0, c1, c2, ., cn such that g(x)=c0f(x)+ c1f'(x)+….

Let f(x) be a polynomial of degree n in Pn(R). Prove that for any g(x) in Pn(R) there exist scalars c0, c1, c2, …, cn such that g(x)=c0f(x)+ c1f'(x)+ c2f”(x)+…+cnf(n)(x).

Let f(x) be a polynomial of degree n in Pn(R). Prove that for any g(x) in Pn(R) there exist scalars c0, c1, c2, ., cn such that g(x)=c0f(x)+ c1f'(x)+…

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