If a polynomial function with all real coefficients has a complex
zero of the form A+Bi, then it also has a complex zero which is the
conjugate of A+Bi which is A-Bi.

Since f has complex zero 4-i, it also has zero 4+i.

Since f has degree 3, it can have no more than 3 zeros.

So the three zeros are 2, 4-i and 4+i

The only remaining zero was 4+i.

Edwin