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Let P4 denote the space of polynomials of degree less than 4 with real coefficients. Show...

Let P4 denote the space of polynomials of degree less than 4 with real coefficients. Show that the standard operations of addition of polynomials, and multiplication of polynomials by a scalar, give P4 the structure of a vector space (over the real numbers R). Your answer should include verification of each of the eight vector space axioms (you may assume the two closure axioms hold for this problem).

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