Write a Linear Factorization of the Function $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 2 x - 5$

question 251

Multiple Choice

Write a linear factorization of the function.
- $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 2 x - 5$

• A) \(f ( x ) = ( x - 1 ) ( 2 x + 3 + \sqrt { 11 } i ) ( 2 x + 3 - \sqrt { 11 } i )\)
• B) \(f ( x ) = ( x + 1 ) ( 2 x + 3 + \sqrt { 7 } i ) ( 2 x + 3 - \sqrt { 7 } i )\)
• C) \(f ( x ) = ( x - 1 ) ( x + 3 + \sqrt { 11 } i ) ( x + 3 - \sqrt { 11 } i )\)
• D) \(f ( x ) = ( x + 1 ) ( 2 x + 3 + \sqrt { 11 } i ) ( 2 x + 3 - \sqrt { 11 } i )\)

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Definitions:

Gonadotropin-releasing Hormone

Gonadotropin-releasing hormone (GnRH) is a hormone released from the hypothalamus that stimulates the pituitary gland to release gonadotropins and regulate reproductive functions.

Somatostatin

A hormone that inhibits the secretion of several other hormones, including growth hormone and insulin.

Hypothalamus

A region of the brain that coordinates both the autonomic nervous system and the activity of the pituitary, controlling body temperature, thirst, hunger, and other homeostatic systems.

Anterior Pituitary

A glandular portion of the pituitary gland that produces and secretes hormones regulating various bodily functions.