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

question 57

Multiple Choice

Use synthetic division to determine the quotient and remainder for the division problem. $\left( x ^ { 5 } + 1 \right) \div ( x + 1 )$

• A) \[Q : x ^ { 4 } + x ^ { 3 } - x ^ { 2 } + x - 1\]
• \(\mathrm { R } : 0\)
• B) \[Q : x ^ { 4 } - x ^ { 3 } + x ^ { 2 } - x + 1\]
• \(\mathrm { R } : 0\)
• C) \[Q : x ^ { 4 } - x ^ { 3 } + x ^ { 2 } - x + 1\]
• \(\mathrm { R } : 1\)
• D) \(\begin{array} { l }
• \mathrm { Q } : x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + x + 1 \\
• \mathrm { R } : - 1
• \end{array}\)
• E) \[\mathrm { Q } : x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + x + 1\]
• \(\mathrm { R } : 0\)

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Definitions:

Money Supply Growth

The increase in the total amount of monetary assets available in an economy at a specific time.

Unemployment Rate

The proportion of the workforce that is unemployed and actively seeking work.

Long-run Phillips Curve

An economic concept that represents the relationship between inflation and unemployment when the effects of short-term shocks have dissipated, showing no trade-off between inflation and unemployment in the long run.

Natural Rate

A concept in economics referring to the level of unemployment at which there is no cyclical or deficient-demand unemployment. It represents a balance between the supply of labor and job vacancies, considering that some frictional and structural unemployment is inevitable.