Question: Let P(4) denote the vector space consisting of all polynomials p(x) of degree 4. (a) Are p1(x) = x3 - 3x + l. p2(x)

Let P(4) denote the vector space consisting of all polynomials p(x) of degree ≤ 4.
(a) Are p1(x) = x3 - 3x + l. p2(x) = x4 - 6x + 3. P3(x) = x4 - 2x3 + 1, linearly independent elements of P(4)?
(b) What is the dimension of the subspace of P(4) spanned by p1, p2, p3?

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