Use Synthetic Division to Determine the Quotient and Remainder for the Division

question 244

Multiple Choice

Use synthetic division to determine the quotient and remainder for the division problem. $\left( 4 x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 7 x - 1 \right) \div ( x + 1 )$

• A) \[Q : 4 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 14\]
• \(\mathrm { R } : 13\)
• B) \[Q : 4 x ^ { 3 } - 5 x ^ { 2 } - 7 x - 14\]
• \(\mathrm { R } : 0\)
• C) \[Q : 4 x ^ { 3 } - 5 x ^ { 2 } - 7 x - 14\]
• \(\mathrm { R } : 13\)
• D) \(\begin{array} { l }
• \mathrm { Q } : 4 x ^ { 3 } - 5 x ^ { 2 } - 7 x - 14 \\
• \mathrm { R } : - 13
• \end{array}\)
• E) \[Q : 4 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 14\]
• \(\mathrm { R } : 0\)

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Definitions:

Carbon-to-hydrogen

The ratio of carbon atoms to hydrogen atoms in a molecule.

Carbon-to-oxygen

A ratio that compares the amount of carbon atoms to oxygen atoms in a molecule or compound.

Enzymatic Addition

A process by which enzymes facilitate the addition of certain groups to molecules, altering their function or activity.

Large Molecules

Macromolecules formed by the joining of smaller molecules, often complex structures essential for life, like proteins, nucleic acids, carbohydrates, and lipids.