$\"\"$

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The function is $\"\"$ .

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Graph :

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Draw the coordinate plane.

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Graph the function $\"\"$ .

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$\"\"$

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Observe the graph:

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Locate the points on the grapgh where the function touches $\"\"$ -axis.

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From the graph, it appears that $\"\"$ are reasonable.

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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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$\"\"$

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Perform the synthetic substitution method on the depressed polynomial by testing $\"\"$ .

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$\"\"$

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The remaining quadratic factor is $\"\"$ .

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The remaining quadratic factor can be written as $\"\"$ .

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Factor $\"\"$ by writing the expression first as a difference of squares $\"\"$ or $\"\"$ .

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Factored form of $\"\"$ is $\"\"$ .

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Factored form of $\"\"$ is $\"\"$ .

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The zeros of the depressed polynomial are $\"\"$ .

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$\"\"$

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Therefore, $\"\"$ are the factors of $\"\"$ .

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By using Factor theorem,

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When $\"\"$ then $\"\"$ is a factor of polynomial.

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Factored form of $\"\"$ .

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So $\"\"$ has five real zeros.

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Zeros are $\"\"$ .

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$\"\"$

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The linear factorization of $\"\"$ is $\"\"$ .

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Zeros are $\"\"$ .