SOLUTION: 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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 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      Log On


   

Question 582207: 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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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.
:
Revenue: r(x) = 7x^3 + 6x^2 - 6x - 3
Costs: c(x) = 6x^2 - 9x + 9
:
Profit (p) = Revenue - cost, therefore:
p(x) = (7x^3 + 6x^2 - 6x - 3) - (6x^2 - 9x + 9)
removing the brackets
p(x) = 7x^3 + 6x^2 - 6x - 3 - 6x^2 + 9x - 9
combine like terms
p(x) = 7x^3 + 6x^2 - 6x^2 - 6x + 9x - 3 - 9
:
p(x) = 7x^3 + 3x - 12; is the profit