Bob’s Barber Shop estimates their gross revenue for the second quarter to be given by the polynomial 8x3 – x2 – 2x + 4. The shop estimates their costs for that quarter to be given by x2 – 4x + 7. For the second quarter, find and simplify a polynomial that will represent their profit.

P=(8X^3 -X^2 - 2X + 4) -(X^2 - 4X + T),

P = 8X^2 - 2X^2 + 2X - 3.

CORRECTION:

P=(8X^3 -X^2 -2X + 4) -(X^2 - 4X + 7),
P = 8X^3 - 2X^2 + 2X - 3.

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

Given that the gross revenue is 8x^3 – x^2 – 2x + 4 and the costs are x^2 – 4x + 7, we can subtract the costs from the gross revenue to get the profit.

Profit = Gross Revenue - Costs

Profit = (8x^3 – x^2 – 2x + 4) - (x^2 – 4x + 7)

To simplify this expression, we can first distribute the negative sign to all terms in the parentheses:

Profit = 8x^3 – x^2 – 2x + 4 - x^2 + 4x - 7

Now, let's combine like terms:

Profit = 8x^3 + (-x^2 - x^2) + (-2x + 4x) + (4 - 7)

Simplifying further:

Profit = 8x^3 - 2x^2 + 2x - 3

Therefore, the polynomial that represents the profit for the second quarter is 8x^3 - 2x^2 + 2x - 3.