Bob's Barber shop estimates their gross revenue for the second qaurter to be given by the polynomial 9x^3+4x^2-6x+9. The shop estimates their costs for that quarter to be given by 7x^2+2x+1. For the second qauter,find and simplify a polynomial that will represent their profit
You have to subract the second equation from the first equation. Make sure to put the second equation in parenthases and distrbute the negative sign!
To find the profit, we need to subtract the costs from the gross revenue. So, we will subtract the polynomial for costs - 7x^2+2x+1, from the polynomial for gross revenue - 9x^3+4x^2-6x+9.
(9x^3+4x^2-6x+9) - (7x^2+2x+1)
To simplify, we combine like terms by combining the coefficients of the same degree.
For the x^3 term, we have 9x^3 - there is no like term in the costs polynomial, so it remains as is.
For the x^2 term, we have 4x^2 - 7x^2 = -3x^2.
For the x term, we have -6x - 2x = -8x.
For the constant term, we have 9 - 1 = 8.
Combining these terms, the simplified polynomial for the profit is:
9x^3 - 3x^2 - 8x + 8.