$\"\"$

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The function is $\"\"$ .

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Rational zeros method:

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Rational Root Theorem, if a rational number in simplest form $\"\"$ is a root of the polynomial equation $\"\"$ , then $\"\"$ is a factor of $\"\"$ and $\"\"$ is a factor if_{$\"\"$ .}

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If $\"\"$ is a rational zero, then $\"\"$ is a factor of $\"\"$ and $\"\"$ is a factor of $\"\"$ .

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

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The possible values for $\"\"$ are $\"\"$ .

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

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$\"\"$

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The function is $\"\"$ .

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

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$\"\"$

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The depressed polynomial is $\"\"$ .

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

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

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$\"\"$

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

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The depressed polynomial is $\"\"$ .

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The equation $\"\"$ has no real solutions.

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By Factor theorem, when $\"\"$ then $\"\"$ is a factor of polynomial.

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Therefore,

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$\"\"$

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Thus, the real zeros $\"\"$ are $\"\"$ and $\"\"$ .

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Factor form of $\"\"$ is $\"\"$ .

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$\"\"$

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The real zeros of $\"\"$ are $\"\"$ and $\"\"$ .

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Factor form of $\"\"$ is $\"\"$ .