Let R = R[x] be the ring of real polynomials in the variable x, and let I = be the ideal of R generated by 2². For an integer d≥ 1, we denote by Rd the set of polynomials in R of degree less or equal than d. Show that the set V = {(f, g) € R₁ × Rd : f g € I} is an R-module (i.e., V is a real vector space), where r(f, g) = (rf, rg), for r ER and (f, g) € V.

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