Use the Factor Theorem to Determine Whether X - C $$f ( x ) = 2 x ^ { 3 } + 16 x ^ { 2 } + 39 x + 45 ; c = - 5$$

question 128

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) .
- $$f ( x ) = 2 x ^ { 3 } + 16 x ^ { 2 } + 39 x + 45 ; c = - 5$$

• A) No
• B) Yes; \(f ( x ) = ( x - 5 ) \left( 2 x ^ { 2 } + 6 x - 9 \right)\)
• C) Yes; \(f ( x ) = ( x + 5 ) \left( 2 x ^ { 2 } + x + 9 \right)\)
• D) Yes; \(f ( x ) = ( x + 5 ) \left( 2 x ^ { 2 } + 6 x + 9 \right)\)

---

Definitions:

Demand Increased

A situation where the desire or need for a product or service rises, leading to potentially higher prices and/or increased production.

Quantity Demanded

The overall volume of a good or service that individuals are prepared and capable of buying at a given price.

Demand Decreased

A situation where the desire or need for a particular product or service declines.

Demand Increased

A situation where the desire to purchase goods and services at a given price level rises, leading to higher quantity demanded.