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The next three questions refer to subsets of the set of real polynomials defined over the real…

The next three questions refer to subsets of the set of real polynomials defined over the real…

The next three questions refer to subsets of the set of real polynomials defined over the real line (e.g., 3+2t+6t2). Tell which of these subsets are vector spaces. If the subset is not a vector space, identify which of the 10 criteria are not satisfied.i. Polynomials of degree 5 or less.ii. Polynomials that are positive for positive t.iii. Polynomials that go to zero as t goes to zero.