How should I use factor to factor expression over irrational numbers?

For example,
x^2-4 produces (x-2)(x+2)
x^2-2 produces (x-sqrt(2))(x+sqrt(2))
x^4+1 produces (x^2-sqrt(2) x+1) (x^2+sqrt(2) x+1)
x^2+1 produces x^2+1 (only complex roots)
x^4-9 x^2-22 produces (x^2+2)(x-sqrt(11))(x+sqrt(11))

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