Use the Intermediate Value Theorem to Determine Whether the Polynomial $f ( x ) = 3 x ^ { 4 } - 5 x ^ { 3 } + 25 x ^ { 2 } - 45 x - 18$

question 42

Multiple Choice

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
- $f ( x ) = 3 x ^ { 4 } - 5 x ^ { 3 } + 25 x ^ { 2 } - 45 x - 18$

• A) \(f ( x ) = ( 3 x + 1 ) ( x - 2 ) ( x + 3 ) ( x - 3 )\)
• B) \(f ( x ) = ( 3 x + 1 ) ( x - 2 ) ( x + 3 i ) ( x - 3 i )\)
• C) \(f ( x ) = ( 3 x - 1 ) ( x + 2 ) ( x + 3 i ) ( x - 3 i )\)
• D) \(f ( x ) = ( 3 x - 1 ) ( x + 2 ) ( x + 3 ) ( x - 3 )\)

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Definitions:

Ctenophora

Also known as comb jellies, a phylum of invertebrate marine animals characterized by their gelatinous bodies and rows of ciliary plates for locomotion.

Diploblastic

Animal body plan in which there are only two embryonic tissue layers, the ectoderm and endoderm. Compare with triploblastic.

Cnidocytes

Specialized cells found in cnidarians (e.g., jellyfish) that contain a stinging structure used for capturing prey and defense.

Nemertea

A phylum of invertebrate animals known as ribbon worms or proboscis worms, characterized by their elongate bodies and a unique proboscis apparatus.