Find All Real Zeros of the Polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 36 x - 108$

question 443

Multiple Choice

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 36 x - 108$ and determine the multiplicity of each.

• A) \(x = 6 , \text { multiplicity } 2 ; x = - 3 \text {, multiplicity } 1\)
• B) \(x = 6 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1\)
• C) \(x = - 3 \text {, multiplicity } 2 ; x = - 6 \text {, multiplicity } 1\)
• D) \(x = - 6 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1\)
• E) \(x = - 3 \text {, multiplicity } 3\)

---

Definitions:

Ulcer

A lesion that forms in the wall of the stomach or of the duodenum.

Hypotension

A medical condition characterized by blood pressure that is too low, which can lead to symptoms like dizziness or fainting.

Illness Anxiety Disorder

A disorder characterized by excessive worry about having a serious, undiagnosed medical condition despite few or no symptoms and frequent medical reassurance.

Bodily Functions

Bodily functions refer to the physiological processes and activities performed by the body's systems, including digestion, respiration, circulation, and reproduction.