$\"\"$

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The function is $\"\"$ , zero $\"\"$ .

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

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Thus conjugate of $\"\"$ is $\"\"$ .

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$\"\"$ .

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$\"\"$ is a one of factor of the function $\"\"$ .

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Find the other cubic factor by using long division.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Identify Possible Rational Zeros of $\"\"$ :

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

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

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The polynomial function is $\"\"$ .

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Use rational zero theorem to find the potential rational zeros of a polynomial function.

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If $\"\"$ is the rational zero, then $\"\"$ is factor of the constant term $\"\"$ and $\"\"$ is factor of the leading coefficient $\"\"$ .

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The possible values of $\"\"$ are $\"\"$ , and $\"\"$ .

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The possible values of $\"\"$ are $\"\"$ , and $\"\"$ .

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Now form all possible ratios of $\"\"$ are,

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ is a one of factor of the function $\"\"$ .

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$\"\"$ is a zero of $\"\"$ .

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Find the other quadratic factor by using long division.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Factor the equation $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ are zeros of $\"\"$ .

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Remaining zeros are $\"\"$ .

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$\"\"$

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Remaining zeros are $\"\"$ .