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
)
(Foil method)
(Simplify)
(Combine like terms)
(Distributive property:
)
(Simplify)
(Combine like terms)
Therefore the polynomial function is
.
The polynomial function is
.