Divide Using Synthetic Division $$\left( x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } - x + 40 \right) \div ( x + 2 )$$

question 420

Multiple Choice

Divide using synthetic division.
- $$\left( x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } - x + 40 \right) \div ( x + 2 )$$

• A) \(x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } - 9 x + 17 + \frac { 6 } { x + 2 }\)
• B) \(x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } - 9 x - 17 + \frac { 6 } { x + 2 }\)
• C) \(x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } - 10 x + 17 + \frac { 11 } { x + 2 }\)
• D) \(x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } - 10 x - 18 + \frac { 11 } { x + 2 }\)

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Definitions:

Tollin's Test

A qualitative chemical test used to differentiate between aldehydes and non-reactive ketones based on the reduction of ammoniacal silver nitrate.

Glycosidic Linkages

Bonds that connect sugar molecules in carbohydrates, formed between hydroxyl groups of two sugar molecules.

Ruff Degradation

A chemical reaction used to shorten the carbon chain of sugars by one carbon atom through oxidation.

Optically Active

Describes compounds that have the ability to rotate the plane of polarized light, a property often associated with the presence of chiral centers.