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

---

Definitions:

PhCHO

Refers to the chemical compound benzaldehyde, which consists of a benzene ring bonded to an aldehyde group.

PhCOCl

Commonly referred to as benzoyl chloride, it's a compound consisting of a benzene ring attached to a carbonyl chloride group, used in organic synthesis.

Mechanistic Step

Refers to an individual stage or transition within the broader sequence of events that constitute a chemical reaction's mechanism.

Amine

An organic compound and functional group consisting of a basic nitrogen atom with a lone pair and deriving from ammonia by replacement of one or more hydrogen atoms by organic groups.