Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = 5 x ^ { 4 } - 8 x ^ { 3 } + 23 x ^ { 2 } - 32 x + 12$$

question 233

Multiple Choice

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
- $$f ( x ) = 5 x ^ { 4 } - 8 x ^ { 3 } + 23 x ^ { 2 } - 32 x + 12$$

• A) \(- 4 , - 1,1 , \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 3 ) ( x + 1 ) ( x + 4 )\)
• B) \(1 , \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 3 ) \left( x ^ { 2 } + 4 \right)\)
• C) \(4 , \frac { 3 } { 5 } ; f ( x ) = ( x - 4 ) ( 5 x - 3 ) \left( x ^ { 2 } + 1 \right)\)
• D) \(- 4 , - 1,1 , - \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x + 3 ) ( x + 1 ) ( x + 4 )\)

---

Definitions:

Honest

The quality of being truthful, sincere, and free from deceit or fraud.

Self-monitoring

The practice of paying attention to one's own behavior and its effects on others, with the potential to adjust behavior based on social cues.

Judged

Considered or deemed to be in a certain way, often involving forming an opinion or evaluation.

Depressed

A mood disorder characterized by persistent feelings of sadness, hopelessness, and a lack of interest or pleasure in activities.