Let Pn be the set of real polynomials of degree at most n. Show that is a subspace of P5- S = {p € P5 : x² + 3x + 1 is a

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Let Pn Be The Set Of Real Polynomials Of Degree At Most N Show That Is A Subspace Of P5 S P P5 X 3x 1 Is A 1 (17.51 KiB) Viewed 28 times

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Let Pn be the set of real polynomials of degree at most n. Show that is a subspace of P5- S = {p € P5 : x² + 3x + 1 is a factor of of p(x)} 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