Find All Zeros of the Function and Write the Polynomial $$f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 26$$

question 285

Multiple Choice

Find all zeros of the function and write the polynomial as a product of linear factors.
- $$f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 26$$

• A) \(f ( x ) = ( x + 1 ) ( x + 5 + i \sqrt { 2 } ) ( x - 1 - i \sqrt { 2 } )\)
• B) \(f ( x ) = ( x + 1 ) ( x + 5 + i ) ( x + 5 - i )\)
• C) \(f ( x ) = ( x + 1 ) ( x + 5 + i ) ( x - 5 - i )\)
• D) \(f ( x ) = ( x - 1 ) ( x + 5 + i \sqrt { 2 } ) ( x + 5 - i \sqrt { 2 } )\)

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Definitions:

Polypeptide Chain

A series of amino acids linked together by peptide bonds, forming part of or the whole primary structure of a protein.

mRNA

Messenger RNA, a type of RNA that carries genetic information from DNA to the ribosome, where it serves as a template for protein synthesis.

Ribosome

A cellular organelle composed of RNA and proteins, found throughout the cytoplasm in cells, which is involved in decoding the mRNA to produce proteins.

Nucleic Acid Bases

The parts of DNA and RNA molecules that carry genetic information, specifically adenine, thymine (in DNA), cytosine, guanine, and uracil (in RNA).