Bob barber shop estimates their gross revenue for the second quarter to be given by the polynimal 3x^3+6x^2+3x+3. The shop estimates their cost for the quarter to be given by 9x^2-6x+5. Find and simplify the polyminal that will represent their profit. Will someone show me how to do this?
Profit = gross revenue - cost
Gross revenue = 3x^3+6x^2+3x+3
Cost = 9x^2-6x+5
Profit (group like terms and add)
= 3x^3+6x^2+3x+3 -(9x^2-6x+5)
= 3x^3+6x^2+3x+3 - 9x^2+6x-5
= 3x³ + 6x²-9x² +3x+6x +3-5
= 3x³ - 3x³ + 9x -2
To find the profit, we need to subtract the cost from the revenue.
Given that the revenue polynomial is 3x^3 + 6x^2 + 3x + 3, and the cost polynomial is 9x^2 - 6x + 5, we can subtract the cost from the revenue as follows:
(3x^3 + 6x^2 + 3x + 3) - (9x^2 - 6x + 5)
To simplify this expression, we can distribute the negative sign to every term in the parentheses:
3x^3 + 6x^2 + 3x + 3 - 9x^2 + 6x - 5
Now, combine like terms:
(3x^3) + (6x^2 - 9x^2) + (3x + 6x) + (3 - 5)
This simplifies to:
3x^3 - 3x^2 + 9x - 2
Therefore, the polynomial that represents the shop's profit is 3x^3 - 3x^2 + 9x - 2.