Solve the Problem Using Matrices $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$

question 23

Multiple Choice

Solve the problem using matrices.
-Find the function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ for which $f ( 0 ) = - 2 , f ( 1 ) = 5 , f ( - 1 ) = 3$ , $f ( 2 ) = 4$ .

• A) \(f ( x ) = 10 x ^ { 3 } - 18 x ^ { 2 } - 13 x + 6\)
• B) \(f ( x ) = - 8 x ^ { 3 } + 12 x ^ { 2 } + 5 x - 6\)
• C) \(f ( x ) = - \frac { 10 } { 3 } x ^ { 3 } + 6 x ^ { 2 } + \frac { 13 } { 3 } x - 2\)
• D) \(f ( x ) = \frac { 8 } { 3 } x ^ { 3 } + 4 x ^ { 2 } + \frac { 5 } { 3 } x - 2\)

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Definitions:

Book Value Method

An accounting technique that determines the value of an asset or company based on the figures in the company's balance sheet, primarily using historical costs minus depreciation.

Conversion Losses

Losses incurred when converting assets from one form to another, often related to currency exchange rates or physical transformation processes.

Treasury Stock

Shares that were issued and subsequently repurchased by the issuing company, reducing the amount of outstanding stock on the open market.

Complex Capital Structure

A financial structure that includes various forms of securities, such as different classes of stock and convertible securities, which can affect the computation of earnings per share.