When I want to factor a polynomial, say $ p (x) $ finished $ mathbb {Q}[sqrt{2}]$,

I can do

`Factor[p(x), Extension -> {Sqrt[2]}]`

What happens if I want to factor a polynomial with more than one variable $ p (x, y, z) $ over a *specific* field, let's say $ mathbb {F} _2[x,y,z]$?

where $ mathbb {F} _2 $ It is the field with 2 elements.