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 .

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 is a one of the factor of the function .

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 integer factors of the constant term .

or .

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.

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Multiply the numerator, denominator of the complex fraction by y

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Consider which can be written as .

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The remaining roots of the function  are  and .

The remaining roots of the function  are  and .