Problem 4 We have seen that R3[X]| = {set of polynomials of degree at most 3} is a R- vector space, being a vector subspace of the space of polynomials R[X]. Consider the following subsets of R3[X]: V = {set of polynomials ag +a1 X +a2 X% +a3X?3, such that ag+ 1 2 UNIVERSITY OF MIAMI, SPRING 2024 a3 = 0} and W = {set of polynomials P, such that P(1) = 0}. (1) Show that V and W are vector subspaces of R3[X]. (2) Let us define U = {set of polynomials P = ap+a; X +a3X?%+a3X?, such that ag+as = 0 and P(1) =0} Show that U is a vector subspace of R3|z]