The polynomial function is  and zero : .

The root of the function is .

From the conjugate pair theorem, complex zeros occur in conjugate pairs.

Thus conjugate of is .

.

is a factor of .

Identify Possible Rational Zeros :

Usually it is not practical to test all possible zeros of a polynomial function using only synthetic

substitution.

The Rational Zero Theorem can be used for finding the some possible zeros to test.

The function is .

Because the leading coefficient is , the possible rational zeros are the intezer factors of the constant term .

Therefore the possible rational zeros of are

.

Since  is a known root, divide the polynomial by  to find the quotient polynomial.

This polynomial can then be used to find the remaining roots.

.

.

The polynomial can be written as set of linear factors.

.

The zereos are

The remaining roots of the function are and .

The remaining roots of the function are and .