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

question 66

Multiple Choice

Use synthetic division to determine the quotient and remainder for the division problem. $\left( 4 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 1 \right) \div \left( x + \frac { 1 } { 2 } \right)$

• A) Q: \(4 x ^ { 2 } - 2 x + 7\)
• R: 0
• B) Q: \(4 x ^ { 2 } - 2 x + 7\)
• R: \(\frac { 9 } { 2 }\)
• C) \(\begin{array} { l }
• \mathrm { Q } : 4 x ^ { 2 } + 2 x - 7 \\
• \mathrm { R } : - \frac { 9 } { 2 }
• \end{array}\)
• D) \(\begin{array} { l }
• \mathrm { Q } : 4 x ^ { 2 } - 2 x + 7 \\
• \mathrm { R } : - \frac { 9 } { 2 }
• \end{array}\)
• E) Q: \(4 x ^ { 2 } + 2 x - 7\)
• \(\mathrm { R } : \frac { 9 } { 2 }\)

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Definitions:

Hardy-Weinberg Principle

A foundational principle in population genetics stating that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences.

Genetic Drift

A mechanism of evolution in which allele frequencies of a population change over generations due to chance or random events.

Small Populations

Populations with a small number of individuals, which may face increased risks of extinction due to genetic drift, inbreeding, and reduced genetic diversity.

Genetic Isolation

A situation where different populations of a species are unable to interbreed, often leading to the formation of new species.