Use the Factor Theorem to Determine Whether X - C $$f ( x ) = x ^ { 6 } - 12 x ^ { 4 } - 69 x ^ { 2 } + 80 ; c = 4$$

question 323

Multiple Choice

Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the
form f(x) = (x - c) (quotient) .
- $$f ( x ) = x ^ { 6 } - 12 x ^ { 4 } - 69 x ^ { 2 } + 80 ; c = 4$$

• A) Yes; \(f ( x ) = ( x - 4 ) \left( x ^ { 5 } - 5 x ^ { 4 } + 5 x ^ { 3 } + 16 x ^ { 2 } - 5 x - 20 \right)\)
• B) No
• C) Yes; \(f ( x ) = ( x - 4 ) \left( x ^ { 5 } + 4 x ^ { 4 } - 4 x ^ { 3 } + 20 x ^ { 2 } - 5 x - 20 \right)\)
• D) Yes; \(f ( x ) = ( x - 4 ) \left( x ^ { 5 } + 4 x ^ { 4 } + 4 x ^ { 3 } + 16 x ^ { 2 } - 5 x - 20 \right)\)

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Definitions:

Market Rate

The ongoing market rate at which you can buy or sell an asset or service.

Contract Rate

The interest rate stated in a loan or lease agreement, dictating the rate at which interest accrues on the outstanding principal.

Bond Premium

The excess of a bond's market price over its principal amount or nominal value.

Straight-line Method

A strategy for computing depreciation or amortization through evenly apportioning the cost of an asset across its expected useful duration.