A Factor the Expression $x ^ { 3 } - 27$

question 7

Multiple Choice

a. Factor the expression $x ^ { 3 } - 27$
b. Use the zero product rule and the quadratic formula to solve the equation $x ^ { 3 } - 27 = 0$ = 0. There should be three solutions.

• A) a. \(( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)\)
• b. \(\left\{ 3 , \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}\)
• B) a. \(( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)\)
• b. \(\left\{ 3 , - \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}\)
• C) a. \(( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)\)
• b. \(\left\{ 3 , \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}\)
• D) a. \(( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)\)
• b. \(\left\{ 3 , - \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}\)

---

Definitions:

Unit Elasticity

Unit elasticity refers to a situation where a change in the price of a good or service results in a proportionally equal change in the quantity demanded or supplied, indicating a unitary elasticity of demand or supply.

Maximum Total Revenue

The highest possible earnings that a firm can achieve from the sale of goods or services, typically found by optimizing price and quantity sold.

Price

The price necessary to acquire a good or service.

Demand Curve

A graphical representation of the relationship between the price of a good or service and the quantity demanded by consumers.