Question

Darnell and Stephanie have competing refreshment stand businesses. Darnell’s profit can be modeled with the polynomial, (c²) + 8c - 100, Where C is the number of items sold. Stephanie’s profit can be modeled with the polynomial, 2c² - 7c - 200.

A. Polynomial for the difference: -c² + 15c + 100
B. Polynomial for combined earnings: 3c² + c - 300
C. Polynomial for the difference: c² - 15c + 100
D. Polynomial for combined earnings: 3c² - c - 300

Answer 1

The polynomial for the difference in earnings is -c² + 15c + 100. The polynomial for the combined earnings is 3c² + c - 300.

Step-by-step explanation:

The polynomial for Darnell's profit is (c²) + 8c - 100, and the polynomial for Stephanie's profit is 2c² - 7c - 200.

To find the polynomial for the difference in their earnings, we subtract Stephanie's profit polynomial from Darnell's profit polynomial. So the polynomial for the difference is (c²) + 8c - 100 - (2c² - 7c - 200). Simplifying this expression, we get -c² + 15c + 100.

To find the polynomial for their combined earnings, we add Darnell's profit polynomial and Stephanie's profit polynomial. So the polynomial for the combined earnings is (c²) + 8c - 100 + (2c² - 7c - 200). Simplifying this expression, we get 3c² + c - 300.