$\"\"$

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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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Because the leading coefficient is $\"\"$ , the possible rational zeros are the integer factors of the constant term $\"\"$ .

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

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$\"\"$

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$\"\"$

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

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$\"\"$

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$\"\"$ is a rational zero.

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The depressed polynomial is $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$ is a rational zero.

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

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The final quotient is $\"\"$ .

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$\"\"$ has no real zeros.

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

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$\"\"$

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Possible rational zeros of $\"\"$ are

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$\"\"$ .

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