Respuesta :

Answer:

[tex](x+2-\sqrt{9}) , (x-2+\sqrt{9}) ,(x-9)[/tex]

Step-by-step explanation:

Given that f(x) is a polynomial function.

This implies that f(x) has x terms of positive integral degrees and also rational coefficients only.

Since an irrational root is given a root of f(x), we find that its conjugate also should be a root of f(x)

i.e. If [tex]-2+\sqrt{8}[/tex] is a root, then [tex]-2-\sqrt{8}[/tex] is also a root.

(Because this only when multiplied will make coefficients rational)

So the factors of f(x) should be atleast

[tex](x+2-\sqrt{9}) , (x-2+\sqrt{9}) ,(x-9)[/tex]

There can be other factors also but this is compulsory

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