Find the Zeros for the Polynomial Function and Give the Multiplicity

question 237

Multiple Choice

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each zero.
- $$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$$

• A) \(- 1\), multiplicity 1 , crosse the \(x\)-axis;
• 1 , multiplicity 1 , crosses the \(x\)-axis;
• - 8 , multiplicity 1 , crosses the \(x\)-axis.
• B) 8 , multiplicity 1 , crosses the x-axis;
• 1 , multiplicity 1 , crosses the \(x\)-axis;
• - 8 , multiplicity 1 , crosses the \(x\)-axis.
• C) 1 , multiplicity 2 , touches the \(x\)-axis and turns around;
• \(- 8\), multiplicity 1 , crosses the x-axis.
• D) \(- 1\), multiplicity 1 , touches the \(x\)-axis and turns around; 1 , multiplicity 1 , touches the \(x\)-axis and turns around;
• - 8 , multiplicity 1 , touches the \(x\)-axis and turns around Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible.

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