$\"\"$

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The function is $\"\"$ .

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Let $\"\"$ .

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Perform the synthetic division 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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The remaining factor can be written as $\"\"$ .

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$\"\"$

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$\"\"$ $\"\"$

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Therefore $\"\"$ has $\"\"$ real zeros at $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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Create a sign chart using these values.

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$\"\"$

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Note : The hallow circles denote that the values are not included in the solution set.

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Observe the sign chart :

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The set of values of $\"\"$ denoted in blue color represents the solution set.

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Determine whether $\"\"$ is positive or negative on the test intervals.

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Test intervals are $\"\"$ and $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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If $\"\"$ ,then $\"\"$ .

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The solutions of $\"\"$ are $\"\"$ values such that $\"\"$ is positive.

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$\"\"$ is positive in the interval $\"\"$ and $\"\"$ .

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The solution is $\"\"$ .

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$\"\"$

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The solution set of $\"\"$ is $\"\"$ .