Let V be set of all polynomials p(x) = ao + a₁x + a²x² + • anx" for which -5 is a root. Mark the vector space axioms that are satisfied by V. (u, v, and w are arbitrary elements of V, and c and d are scalars.) The sum u + v exists and is an element of V. (V is closed under addition.) cu is an element of V. (V is closed under scalar multiplication.) There exists an element of V, called a zero vector, denoted 0, such that u +0=u. For every element u of V there exists an element called a negative of u, denoted -u, such that u + (-u) = 0. None of these For the following axioms, determine whether equality holds assuming the quantities involved are defined and exist in V. Ou+v=v+u (commutative property) Ou + (v+w) = (u + v) + w (associative property) Oc(u + v) = cu + cv (c + d)u = cu + du c(du) = (cd)u lu= u None of these

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