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Prove using induction: If F is any field and f(x)=p1(x)p2(x)...pn(x) is a nonconstant polynomaial of the field,...

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Advance Math

Prove using induction:

If F is any field and f(x)=p1(x)p2(x)...pn(x) is a nonconstantpolynomaial of the field, f an element of F, and p1,...,pn areirreducible factors of the field.

Then, there exists a field L such that f factors into linearfactors over L.

Hint: start with p1(x) to prove that F is a subset of someK1=F[x]/((p1)) , then induct.

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