Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = x ^ { 4 } - 5 x ^ { 2 } - 36$$

question 272

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.
- $$f ( x ) = x ^ { 4 } - 5 x ^ { 2 } - 36$$

• A) \(3 ; f ( x ) = ( x - 3 ) ^ { 2 } \left( x ^ { 2 } + 4 \right)\)
• B) \(- 3,3 ; f ( x ) = ( x - 3 ) ( x + 3 ) \left( x ^ { 2 } + 4 \right)\)
• C) \(- 3 , - 2,3,2 ; f ( x ) = ( x - 3 ) ( x + 3 ) ( x - 2 ) ( x + 2 )\)
• D) \(- 2,2 ; f ( x ) = ( x - 2 ) ( x + 2 ) \left( x ^ { 2 } + 9 \right)\)

---

Definitions:

Patent

A government-granted exclusive right to an inventor, allowing them to prevent others from making, using, or selling their invention for a certain period.

Takeover Bid

In corporate law, the offer to buy the voting stock of a corporation.

Friendly Suitor

An entity or person who proposes a takeover or merger that is welcomed by the target company's board.