Let ?n be the set of real polynomials of degree at most n. Show that S = {p ? ?7 : x^2 + 5x + 8 is a factor of p(x)} is a subspace of ?7.
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First, we need to check if the zero vector (the zero polynomial) is in S. The zero polynomial is a polynomial of degree 0, and it has x^2 + 5x + 8 as a factor since it is the product of x^2 + 5x + 8 and the zero polynomial. So, the zero vector is in S. Show more…
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