The zeroes of the polynomial function are .

If is a zero, then is also a zero.

According to the complex conjugate theorem,

Therefore,  are factors of the polynomial function.

The polynomial function as a product of its factors is .

Solve the equation.

      (write the equation)

       (Regroup terms)

                         (Difference of squares)

                              (Substitute )

                      (Square terms)

                            (Combine like terms)

          (Foil method)

                                (Simplify)

Distributive property:.

                                (Combine like terms)

Therefore the polynomial function is .

The polynomial function is .