Let F be a field and let p(x), a1(x), a2(x), . . . , ak(x) ∈ F[x], wherep(x) is irreducible over F. If p(x) | a1(x)a2(x) ... ak(x), show thatp(x) divides some ai(x).

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Q: 10. Let F(a) be the field described in Exercise 8. Show that a² and a² + a are zeros of x³ + x + 1.

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