Bob’s Barber Shop estimates their gross revenue for the second quarter to be given by the polynomial 7x3 + 6x2 – 6x – 3. The shop estimates their costs for that quarter to be given by 6x2 – 9x + 9. For the second quarter, find and simplify a polynomial that will represent their profit.

its 5

7x3+6x2-2

To find the profit for the second quarter, we need to subtract the costs from the gross revenue.

Given that the gross revenue is represented by the polynomial 7x^3 + 6x^2 - 6x - 3, and the costs are represented by the polynomial 6x^2 - 9x + 9, we can subtract the costs from the gross revenue to get the profit.

So the polynomial that represents their profit for the second quarter will be (7x^3 + 6x^2 - 6x - 3) - (6x^2 - 9x + 9).

To simplify, we need to combine like terms by adding or subtracting coefficients of the same degree.

First, let's remove the parentheses and distribute the negative sign to each term in the second polynomial:

7x^3 + 6x^2 - 6x - 3 - 6x^2 + 9x - 9

Now, let's combine like terms:

7x^3 + (6x^2 - 6x^2) + (-6x + 9x) + (-3 - 9)

Simplifying further:

7x^3 + 0x^2 + 3x - 12

Therefore, the polynomial that represents their profit for the second quarter is 7x^3 + 3x - 12.