Question: Let p = p(x) and q = q(x) be polynomials in p2. Show that is an inner product on p2. Is this an inner product

Let p = p(x) and q = q(x) be polynomials in p2. Show that
(P, a) = p(0)q(0) +pa)+ p(1)q(1)

is an inner product on p2. Is this an inner product on P3? Explain.

(P, a) = p(0)q(0) +pa)+ p(1)q(1)

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