Use the Factor Theorem to Determine Whether X - C $$f ( x ) = 2 x ^ { 3 } + 16 x ^ { 2 } + 39 x + 45 ; c = - 5$$

question 128

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) .
- $$f ( x ) = 2 x ^ { 3 } + 16 x ^ { 2 } + 39 x + 45 ; c = - 5$$

• A) No
• B) Yes; \(f ( x ) = ( x - 5 ) \left( 2 x ^ { 2 } + 6 x - 9 \right)\)
• C) Yes; \(f ( x ) = ( x + 5 ) \left( 2 x ^ { 2 } + x + 9 \right)\)
• D) Yes; \(f ( x ) = ( x + 5 ) \left( 2 x ^ { 2 } + 6 x + 9 \right)\)

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Definitions:

Cattell

Raymond Cattell was a psychologist known for his work on personality theory and psychometrics, including the development of several personality tests.

Cattell

Refers to Raymond Cattell, a psychologist known for his work in personality, factor analysis, and the development of several personality assessments.

Freud

Sigmund Freud, an Austrian neurologist and the founder of psychoanalysis, a method for treating psychopathology through dialogue.

Heredity

The passing on of physical or mental characteristics genetically from one generation to another.