The polynomial function is
and its zero
.
Since complex zeros occur in conjugate pairs,
is also a zero of f.
Thus, the factors of f are
.
Multiplying these two factors produces
.
Rewrite the expression in long division form
.
The zero is included for missing term x in the divisor.
\
By the division algorithm theorem, the result of the division is
.
The complete factorization of f(x) is
.
The zeros of f(x) are
.
The zeros of f(x) are
.