$\"\"$

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A polynomial function $\"\"$ of degree $\"\"$ has at most $\"\"$ distinct real zeros and at most $\"\"$ turning points.

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$\"\"$

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The function is $\"\"$ .

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The degree of the function is $\"\"$ .

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Since the degree of the function is $\"\"$ ( $\"\"$ ), the function $\"\"$ has at most $\"\"$ ( $\"\"$ ) distinct real zeros and at most $\"\"$ ( $\"\"$ ) turning points.

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Find the real zeros by equating $\"\"$ to zero.

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Solve the equation $\"\"$ by using factoring.

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$\"\"$

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Apply zero product property.

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$\"\"$

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Thus, the function $\"\"$ has three distinct real zeros at $\"\"$ and $\"\"$ .

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$\"\"$

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Check :

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Graph the function $\"\"$ to confirm these zeros.

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Graph of the function $\"\"$ is :

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$\"\"$

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Observe the above graph :

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The function $\"\"$ has three distinct real zeros at $\"\"$ and $\"\"$ .

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The possible turning points are $\"\"$ .

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$\"\"$

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The number of possible real zeros are $\"\"$ .

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Distinct real zeros are $\"\"$ and $\"\"$ .

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Turning points are $\"\"$ .