Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1 , and zeros of 3 and 1+i

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 \(\boxed{x^3 - 5x^2 + 8x - 6}\).