Use Division to Write the Rational Function in the Form $\frac { 2 x ^ { 3 } - 3 x ^ { 2 } - 2 x + 27 } { x ^ { 2 } + x - 2 }$

question 313

Multiple Choice

Use division to write the rational function in the form q(x) + r(x) /d(x) , where the degree of r(x) is less than the degree of
d(x) . Then find the partial fraction decomposition of r(x) /d(x) .
- $\frac { 2 x ^ { 3 } - 3 x ^ { 2 } - 2 x + 27 } { x ^ { 2 } + x - 2 }$

• A) \(2 x - 9 - \frac { 5 / 3 } { x + 2 } + \frac { 1 / 3 } { x - 1 }\)
• B) \(2 x - 9 - \frac { 13 } { x + 2 } + \frac { 7 } { x - 1 }\)
• C) \(2 x - 5 - \frac { 7 / 3 } { x + 2 } + \frac { 13 / 3 } { x - 1 }\)
• D) \(2 x - 5 - \frac { 1 } { x + 2 } + \frac { 8 } { x - 1 }\)

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Definitions:

Alkoxymercuration

A chemical reaction that introduces an alkoxy group into an alkene to form an ether, typically involving mercury (II) acetate.

Demercuration

A chemical reaction process that removes mercury from an organomercury compound, often used in the context of reductive reactions and organic synthesis cleanup.

Synthesize

The act of chemically uniting simple elements to produce a substance that is more complex.

Ether

A class of organic compounds characterized by an oxygen atom connected to two alkyl or aryl groups, typically used as solvents or in the synthesis of other chemicals.