Find the Partial Fraction Decomposition $\frac { 4 x ^ { 4 } - 4 x ^ { 3 } + 8 x ^ { 2 } - 7 x + 1 } { x ^ { 3 } - x ^ { 2 } + x - 1 }$

question 7

Multiple Choice

Find the partial fraction decomposition. $\frac { 4 x ^ { 4 } - 4 x ^ { 3 } + 8 x ^ { 2 } - 7 x + 1 } { x ^ { 3 } - x ^ { 2 } + x - 1 }$

• A) \(4 x + \frac { 1 } { x + 1 } + \frac { 3 x } { x ^ { 2 } - 1 }\)
• B) \(4 x + \frac { 1 } { x - 1 } + \frac { 3 x } { x ^ { 2 } + 1 }\)
• C) \(3 x + \frac { 1 } { x - 1 } + \frac { 4 x } { x ^ { 2 } + 1 }\)
• D) \(4 x - 4 + \frac { 1 } { x - 1 } + \frac { 3 x } { x ^ { 2 } + 1 }\)
• E) \(4 x + 4 - \frac { 1 } { x - 1 } + \frac { 3 x } { x ^ { 2 } + 1 }\)

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Definitions:

Liquidated Damages

A bona fide estimate of the monetary damages that would flow from the breach of a contract.

Consequential Damages

Indirect damages that do not flow directly from the act but occur as a consequence of the initial act, often involving loss of profit or other secondary losses.

Liquidated Damages

A pre-determined sum agreed upon by parties in a contract as compensation for breach of contract, where actual damages are difficult to ascertain.