I need to write a polynomial functions of least degree with integral coefficients whose zeros include 4 and 1-i

Answer 1

The complex conjugate of a complex zero must also be a zero, so you will have 3 zeros:

4

1 - i

1 + i

f(x) = A(x - 4) [x - (1 - i)] [x - (1 + i)],

where A is a real nonzero integer. You can expand to standard form if you wish. The coefficients will all come out real.