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

question 100

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) \(- 2,2 ; f ( x ) = ( x - 2 ) ( x + 2 ) \left( x ^ { 2 } + 9 \right)\)

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Definitions:

Active Correlation

A concept in genetics suggesting that an individual’s genes encourage them to seek out environments that complement their inherited traits.

Niche-Picking

Choosing environmental conditions that foster one’s genetically transmitted abilities and interests.

Inherited Preferences

Traits or tendencies passed down from parents to offspring, influencing behaviors such as food choices or habitat preferences.

Reproductive Tract

The system of organs within an organism that works together for the purpose of reproduction, including structures such as the ovaries, fallopian tubes, uterus in females, and the testes and vas deferens in males.