Determine All Possible Rational Solutions of the Polynomial Equation $$f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 3 } + 5 x ^ { 2 } + 18$$

question 32

Multiple Choice

Determine all possible rational solutions of the polynomial equation.
- $$f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 3 } + 5 x ^ { 2 } + 18$$

• A) \(\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 6 , \pm 9 , \pm 18\)
• B) \(\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm \frac { 3 } { 2 } , \pm 6 , \pm 9 , \pm \frac { 9 } { 2 } , \pm 18\)
• C) \(\pm 1 , \pm 2 , \pm 3 , \pm 6 , \pm 9 , \pm 18\)
• D) \(\pm 1 , \pm 2 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 6 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 18 }\)

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Definitions:

Mixed Fraction

A whole number and a fraction combined into one “mixed” number.

Improper Fraction

A fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number).

Fluid Ounces

A unit of volume used to measure liquids, approximately 28.4 milliliters in the British Imperial system and 29.6 milliliters in the U.S. system.

Cup

A small, open container used for drinking liquids, typically made of glass, plastic, metal, or ceramic.