Question: Suppose p P(F) and p = 0. Let U = {pq : q P(F)}. (a) Show that dimP(F)/U = deg p. (Note that, although P(F)

Suppose p P(F) and p = 0. Let U = {pq : q P(F)}. (a) Show that dimP(F)/U = deg p. (Note that, although P(F) is infinite, this quotient space is not!) (b) Find a basis of P(F)/U

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