Use the Factor Theorem to Determine Whether X - C $$f ( x ) = 6 x ^ { 3 } + 16 x ^ { 2 } + 18 x - 8 ; c = \frac { 1 } { 3 }$$

question 171

Multiple Choice

Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the
form f(x) = (x - c) (quotient) .
- $$f ( x ) = 6 x ^ { 3 } + 16 x ^ { 2 } + 18 x - 8 ; c = \frac { 1 } { 3 }$$

• A) Yes; \(f ( x ) = \left\{ x - \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 19 x + 24 \right)\)
• B) Yes; \(f ( x ) = \left( x - \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 18 x + 24 \right)\)
• C) Yes; \(f ( x ) = \left( x + \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 18 x - 24 \right)\)
• D) No

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Definitions:

Large Numbers

Numerical values that are significantly larger than those typically used in everyday life, often requiring special notation or systems to express.

Participants

Individuals who take part in a study, experiment, or activity.

Illusory Correlation

The perception of a relationship between two variables when no such relationship exists.

Strange Behavior

Actions or reactions that deviate significantly from what is considered typical or socially acceptable.