"Let Px be union of all polynomials. Choose a an element of R, and define ta : Px --> R by ta(f) = f(a) Let T=ker(Ta). Prove that the map p(x) |--> (x − a)p(x) is a linear, one-to-one, and onto transformation Px --> T ." Is the assertation in the problem correct? If so, how do you prove it?