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3. let v be the vector space of polynomials of degree...

# Question: let v be the vector space of polynomials of degree...

###### Question details

Let V be the vector space of polynomials of degree 3 or less with the usual notion of addition and scalar multiplication. Let S be the subset of V where f ∈ S if, f(1) = 0 and f'(1) = 0.

(a) Prove that S is also a vector space.

(b) Find a basis for S.

(c) Verify that x3 + x2 − 5x + 3 ∈ S and find its coordinates with respect to the basis you found.