Question

determine a polynomial function of degree 3 with real coefficiants whose zeros are -2, 1+i

Answer 1

so you are basically given 3 zeros since you want real coefficiants and the complex zero given is 1+i so 1-i is the other complex zero
so you have 3 zeros -2,1+i,1-i
and yes -2 also a complex number (but we wanted the complex numbers with the imaginary part to be considered above)
so if x=-2 is a zero so x+2 is a factor

Answer 2

you can do the same thing for x=1+i and x=1-i