Step 1 :Given zeros are 3, 1+i and 1-i (since nonreal zeros must occur in conjugate pairs).
Step 2 :The polynomial can be found by multiplying the factors associated with each zero.
Step 3 :The polynomial function of least degree with real coefficients and given zeros is \(x^3 - 5x^2 + 8x - 6\).
Step 4 :This polynomial has a degree of 3, which is the least possible degree given that we have 3 zeros.
Step 5 :It also has a leading coefficient of 1, as required.
Step 6 :Final Answer: The polynomial function of least degree having only real coefficients, a leading coefficient of 1 , and zeros of 3 and 1+i is \(\boxed{x^3 - 5x^2 + 8x - 6}\).