Question

The gross income, in dollars, that a company makes from selling x items can be modeled by the expression 3x2 + 2x + 4. It costs the company 2 - 3x + x2 dollars to make x items. Which expression represents the company's profit if it makes and sells x items? (Note: Profit = Income - Costs)

Answer 1

The expression for the company's income form selling x items is given as

3x^2 + 2x + 4

The expression for the cost of producing x items is given as

2 - 3x + x^2

We know that

Profit = Income - costs

Thus, the expression that represents that ceompany's profit would be

3x^2 + 2x + 4 - (2 - 3x + x^2)

By opening the bracket, it becomes

3x^2 + 2x + 4 - 2 + 3x - x^2

The next step is to collect like terms. Thus, we have

3x^2 - x^2 + 2x + 3x + 4 - 2

2x^2 + 5x + 2

The correct option is the second one