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?

Answer 1

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