$\"\"$

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The equation is $\"\"$ .

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Consider $\"\"$ .

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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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So, $\"\"$ .

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Consider $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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

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Consider $\"\"$ .

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Using synthetic division:

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$\"\"$

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

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

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The depressed polynomial is $\"\"$ .

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$\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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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 of $\"\"$ are $\"\"$ .

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So, $\"\"$ .

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$\"\"$ .

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$\"\"$ , $\"\"$ is not a zero of $\"\"$ .

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$\"\"$

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$\"\"$ , $\"\"$ is not a zero of $\"\"$ .

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Consider $\"\"$ .

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Using synthetic division:

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$\"\"$

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$\"\"$ , $\"\"$ is a zero of $\"\"$ .

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

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The depressed polynomial is $\"\"$ .

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$\"\"$ .

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The solutions of $\"\"$ are imaginary.

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The real solutions of $\"\"$ are $\"\"$ . $\"\"$

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$\"\"$ .