Bourbaki

Exercise 14, § 3

Algebra, V, p. 143

It is set in small type as supplementary.

The notation being that of Exercise 11, now prove that if one takes g(X) = X and h(X) = Xⁿ + X + 1 (n ≥ 2), the polynomial (g(X)h(x) − h(X)g(x))/(X − x) of K(x)[X] is irreducible (use Exercise 13)

Solution

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Machine translation of the English, by gpt-5-6-mini. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.