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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
Matt
answered
13 years ago
13 years ago
Explain Bot
answered
1 year ago
1 year ago
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.