Find the Zeros for the Polynomial Function and Give the Multiplicity

question 162

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.
- $$f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4$$

• A) \(- 1\), multiplicity 1 , touches the \(x\)-axis and turns around; 1 , multiplicity 1 , touches the \(x\)-axis and turns around;
• \(- 4\), multiplicity 1 , touches the \(x\)-axis and turns around
• B) \(- 1\), multiplicity 1 , crosses the \(x\)-axis;
• 1 , multiplicity 1 , crosses the \(x\)-axis;
• \(- 4\), multiplicity 1 , crosses the \(x\)-axis.
• C) 1 , multiplicity 2 , touches the \(x\)-axis and turns around;
• \(- 4\), multiplicity 1 , crosses the \(x\)-axis.
• D) 4 , multiplicity 1 , crosses the \(x\)-axis;
• 1 , multiplicity 1 , crosses the \(x\)-axis;
• \(- 4\), multiplicity 1 , crosses the \(x\)-axis.

---

Definitions:

Unguided Self-discovery

A process where individuals explore and understand their own feelings, thoughts, and actions without structured guidance or intervention.

Fictional Finalism

A concept from Adlerian psychology suggesting that individuals are motivated more by their expectations of the future than by past experiences.

Inferiority Complex

A psychological condition in which a person feels a deep sense of inadequacy and incompetence, often leading to overcompensation in other areas.

Youngest Child

Describes a child who is the last born in the family hierarchy.