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a) Calculate a basis for the subspace N = {p ∈ P3[x] | p'(3) = 0}...

a) Calculate a basis for the subspace N = {p ∈ P3[x] | p'(3) = 0} of P3[x], with explanation. Why is it a basis?

b) Does the set M = {p ∈ P3[x] | p(1) ≥ 0} form a subspace of P3[x]? Why or why not?

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