Question: If F is a field, let S F[x] where f(x) = anxn + an-1xn-l + + a2x2 + a1x + a0 S

If F is a field, let S ⊂ F[x] where f(x) = anxn + an-1xn-l + ∙∙∙∙∙∙ + a2x2 + a1x + a0 ∈ S if and only if an + an-1 + ∙∙∙∙∙∙∙ + a2 + a1 + a0 = 0. Prove that S is an ideal of F[x].

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First for fx a n x n a n1 x n1 a 2 x 2 a 1 x a 0 we have a n a n1 a 2 a 1 a 0 0 if and on... View full answer

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