Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = 4 x ^ { 3 } + 19 x ^ { 2 } - 8 x + 15$$

question 343

Multiple Choice

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
- $$f ( x ) = 4 x ^ { 3 } + 19 x ^ { 2 } - 8 x + 15$$

• A) \(1 , \frac { 4 } { 3 } , - 5 ; f ( x ) = ( 4 x - 3 ) ( x - 1 ) ( x + 5 )\)
• B) \(- 5 , \frac { 3 } { 4 } , 1 ; f ( x ) = ( 4 x - 3 ) ( x - 1 ) ( x + 5 )\)
• C) \(- 1 , \frac { 4 } { 3 } , - 5 ; f ( x ) = ( 4 x - 3 ) ( x - 5 ) ( x + 1 )\)
• D) \(- 1 , \frac { 3 } { 4 } , 5 ; f ( x ) = ( 4 x - 3 ) ( x - 5 ) ( x + 1 )\)

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Definitions:

Sales Mix

The combination of different products or services that a company sells, each contributing to total sales revenue.

Break-even Point

The point at which total costs and total revenue are equal, meaning no net loss or gain is incurred by the business.

Contribution Margin Ratio

The percentage of each sales dollar that remains after variable costs have been deducted, indicating how much contributes towards fixed costs and profit.

Break-even Point

The Break-even Point is the level of production or sales at which the total revenue generated equals the total costs, indicating no profit or loss.