Question

modeling profit using a polynomial expression

the revenue, in dollars, of a company that produces video game systems can be modeled by the expression \\(5x^2 + 2x - 80\\). the cost, in dollars, of producing the video game systems can be modeled by \\(5x^2 - x + 100\\), where \\(x\\) is the number of video game systems sold. if profit is the difference between the revenue and the cost, what expression represents the profit?

profit can be modeled by the polynomial expression dropdown.
if 1,000 video game systems are sold, the company dropdown.

dropdown options for the first blank:
\\(x + 20\\)
\\(x - 180\\)
\\(3x + 20\\)
\\(3x - 180\\)

Explanation:

Define profit function

$$ P(x) = R(x) - C(x) $$

Substitute given polynomial expressions

$$ P(x) = (5x^2 + 2x - 80) - (5x^2 - x + 100) $$

Simplify by combining like terms

$$ P(x) = 5x^2 - 5x^2 + 2x - (-x) - 80 - 100 = 3x - 180 $$

Answer:

Question 1

• x + 20
• x - 180
• 3x + 20
• 3x - 180 (Correct answer)