Here are two examples with ordinary extensions: Factor[1 + x^4, Extension -> Sqrt[2]] Factor[x^2 + 2 Sqrt[3] x + 3, Extension -> Automatic] --- But what about "generalized" extension? This does not work but maybe someone can see a trick to do the job. Factor[3 + 3 x + 5 x^2 - x^3 + Sqrt[1 + x^2] (3 + x^2 + 2 x^3), Extension -> Sqrt[1 + x^2] Explicit example with known factorization: expr = -8 + 17 x + 11 x^2 + 2 x^3 + 6 x^4 + 2 x^5 + Sqrt[2 + x + 2 x^2] (2 - 7 x + 9 x^2 + x^3 + x^4); f1 = (x^...
