How do you write a polynomial function of least degree given the zeros #sqrt6#, #-3+sqrt5#?
To get a polynomial of least degree use just these two factors (and a non-0 constant factor if you wish).
If we wish the polynomial to have integer or rational coefficients, the the conjugates of the given zeros are also zeros.
That would make the zeros:
The factors in this case would be
When we expand, we get
We could also multiply by any non-0 constant.