Question: Can someone help solve this question with extensive mathematical writing Let In be the set of real polynomials of degree at most n. Show that

Can someone help solve this question with extensive mathematical writing

Let In be the set of real polynomials of degree at most n. Show that S = PEPA : x2 + 8x +9 is a factor of p(z) is a subspace of P4 To check that you are on the right track, answer the following questions. . Is S a subset of a known vector space? Yes . Does S contain the zero element? Yes . Is S closed under vector addition? Yes . Is S closed under scalar multiplication? Yes

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