Give the Maximum Number of Zeros the Polynomial Function May $$f ( x ) = x ^ { 6 } - x ^ { 5 } - x ^ { 4 } - 5 x ^ { 3 } + 2 x ^ { 2 } + 2 x + 3$$

question 40

Multiple Choice

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how
many positive and how many negative zeros it may have.
- $$f ( x ) = x ^ { 6 } - x ^ { 5 } - x ^ { 4 } - 5 x ^ { 3 } + 2 x ^ { 2 } + 2 x + 3$$

• A) \(6 ; 2\) or 0 positive zeros; 2 , or 0 negative zeros
• B) 6; 3 or 1 positive zeros; 3 or 1 negative zeros
• C) 6; 2 or 0 positive zeros; 4,2 , or 0 negative zeros
• D) \(6 ; 4,2\), or 0 positive zeros; 2 or 0 negative zeros

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Definitions:

Tropical Rain Forests

Densely wooded areas found near the equator characterized by high rainfall, biodiversity, and a warm climate year-round.

South America

A continent located in the Western Hemisphere, mostly in the Southern Hemisphere, with a rich diversity of ecosystems, cultures, and histories.

Southeast Asia

A geographic region consisting of countries south of China and Japan, including Indonesia, Vietnam, Thailand, Malaysia, and others, known for its cultural diversity and natural beauty.

Tropical Rain Forests

Dense, rain-soaked forests found near the equator, characterized by high biodiversity and a canopy structure, receiving an abundance of rainfall throughout the year.