$\"\"$

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The function is $\"\"$ .

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The factors are $\"\"$ and $\"\"$ .

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Perform the synthetic division method to test each factor.

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Synthetic division for factor $\"\"$ .

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Rewrite the division expression so that the divisor is in the form of $\"\"$ .

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$\"\"$

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$\"\"$

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The obtained divisor is $\"\"$ .

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Now the divisor is in the form of $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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When $\"\"$ is divided by $\"\"$ , the remainder is $\"\"$ .

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So $\"\"$ is a factor of $\"\"$ .

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The depressed polynomial is $\"\"$ .

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$\"\"$

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The obtained depressed polynomial is $\"\"$ .

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Now test the second factor $\"\"$ with the depressed polynomial $\"\"$ .

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Synthetic division for factor $\"\"$ .

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$\"\"$

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When $\"\"$ is divided by $\"\"$ The remainder is $\"\"$ .

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So $\"\"$ is not a factor of $\"\"$ .

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Since $\"\"$ is a factor of $\"\"$ , the quotient in factored form is $\"\"$ $\"\"$ $\"\"$ .

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$\"\"$

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The obtained depressed polynomial is $\"\"$ .

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Perform the synthetic substitution method by testing $\"\"$ .

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$\"\"$

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Since $\"\"$ , conclude that $\"\"$ is a zero of $\"\"$ .

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Therefore, $\"\"$ is a rational zero.

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Therefore, $\"\"$ and $\"\"$ are the factors of $\"\"$ .

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The remaining quadratic expression $\"\"$ can be written as $\"\"$ .

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The quotient can be written in the factored form as $\"\"$ $\"\"$ $\"\"$ or

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$\"\"$ .

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$\"\"$

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$\"\"$ is a factor of $\"\"$ .

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$\"\"$ is not a factor of $\"\"$ .

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The factored form of $\"\"$ or $\"\"$ . \ \