$\"\"$

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The function is $\"\"$ .

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Identify Possible Rational Zeros :

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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.

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$\"\"$ .

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Possible rational zeros $\"\"$ .

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$\"\"$

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Therefore, the possible rational zeros of $\"\"$ are $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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

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$\"\"$

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Since $\"\"$ , conclude that $\"\"$ is not a zero of $\"\"$ .

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

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$\"\"$

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Since $\"\"$ , conclude that $\"\"$ is not a zero of $\"\"$ .

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$\"\"$

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

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$\"\"$

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Since $\"\"$ , conclude that $\"\"$ is not a zero of $\"\"$ .

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

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$\"\"$

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Since $\"\"$ , conclude that $\"\"$ is not a zero of $\"\"$ .

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$\"\"$

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

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$\"\"$

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Since $\"\"$ , conclude that $\"\"$ is not a zero of $\"\"$ .

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

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$\"\"$

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Since $\"\"$ , conclude that $\"\"$ is not a zero of $\"\"$ .

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$\"\"$

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

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$\"\"$

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Since $\"\"$ , conclude that $\"\"$ is not a zero of $\"\"$ .

\

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

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$\"\"$

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Since $\"\"$ , conclude that $\"\"$ is not a zero of $\"\"$ .

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So by using synthetic division, the polynomial $\"\"$ does not have any rational zeros.

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$\"\"$

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Therefore the possible rational zeros of $\"\"$ are $\"\"$ .

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No rational zeros.