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Question 4. Consider the following subsets of the vector space P3 of polynomials of degree 3...

Question 4. Consider the following subsets of the vector space P3 of polynomials of degree 3 or less: S = {p(x) : p(1) = 0} and T = {q(x) : q(0) = 1} Determine if these subsets are vectors spaces with the standard operations for polynomials

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For proving S is vector space, we can also go by long route of proving all properties of vector spaces.

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