Use
mathematical induction to prove that If p(x) in F[x] and deg p(x) =
n, show that...
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Usemathematical induction to prove that If p(x) in F[x] and deg p(x) =n, show that the splitting field for p(x) over F has degree at mostn!.
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Proof We prove this result by induction on the degree of px The case of n 1 is clear as there is no extension so the degree is clearly 1 Assume inductively that for a polynomial gx Ex where E is some field that the splitting field Eg of gx has degree less
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