Use Synthetic Division to Divide F(x) by X - K $$f ( x ) = - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 ; k = 1$$

question 503

Multiple Choice

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k) q(x) + r for
the given value of k.
- $$f ( x ) = - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 ; k = 1$$

• A) \(f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1 \right)\)
• B) \(f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1 \right)\)
• C) \(f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1 \right)\)
• D) \(f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9 \right)\)

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Definitions:

Gustatory System

The sensory system responsible for the perception of taste and flavor, involving the taste buds on the tongue and other related neural pathways.

Taste Cells

Specialized sensory receptor cells located within the taste buds of the tongue, capable of detecting different tastes like sweet, salty, bitter, sour, and umami.

Molecular Substance

A chemical composition made up of molecules, which are groups of atoms bonded together, representing the smallest fundamental unit of a chemical compound that can take part in a chemical reaction.

Supertasters

Individuals who have a heightened sense of taste, particularly for bitter flavors, likely due to a higher density of taste papillae.