Determine All Possible Rational Solutions of the Polynomial Equation $$f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } + 12 x - 8$$

question 94

Multiple Choice

Determine all possible rational solutions of the polynomial equation.
- $$f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } + 12 x - 8$$

• A) \(\pm 1 , \pm 2 , \pm 4 , \pm 8\)
• B) \(\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 4 , \pm 8\)
• C) \(\pm 1 , \pm 2 , \pm 4\)
• D) \(\pm 1 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 8 } , \pm 2\)

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Definitions:

Ppf (Production Possibility Frontier)

A curve depicting all maximum output possibilities for two goods, given a set of inputs and technology, when resources are fully and efficiently utilized.

Efficiently

Achieving maximum productivity with minimum wasted effort or expense.

Production Inefficiency

A situation where resources are not utilized in the best possible manner, resulting in wasted potential output.

Production Possibility Frontier

A graphical representation that shows the maximum combination of two goods or services that can be produced within a given time period, given available resources and technology.