Use the Factor Theorem to Determine Whether X - C $$f ( x ) = 5 x ^ { 4 } - 7 x ^ { 3 } + 17 x ^ { 2 } - 21 x + 6 ; c = 1$$

question 117

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) .
- $$f ( x ) = 5 x ^ { 4 } - 7 x ^ { 3 } + 17 x ^ { 2 } - 21 x + 6 ; c = 1$$

• A) Yes; \(f ( x ) = ( x - 1 ) \left( 5 x ^ { 3 } + 3 x ^ { 2 } + 15 x - 6 \right)\)
• B) Yes; \(f ( x ) = ( x - 1 ) \left( 5 x ^ { 3 } - 2 x ^ { 2 } - 16 x - 6 \right)\)
• C) Yes; \(f ( x ) = ( x - 1 ) \left( 5 x ^ { 3 } - 2 x ^ { 2 } + 15 x - 6 \right)\)
• D) No

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Definitions:

Datum Feature

A physical feature of a part that acts as a reference for measurement and geometry during machining or inspection processes.

RFS

Requirement for the feature size; a specification in geometric tolerancing where size is a factor.

Runout Tolerance

A type of geometric tolerance that controls the variation of a feature's surface as it rotates about a datum axis.

Surface Profile

Describes the quantifiable variation, texture, or roughness of a surface over a specified area.