Mr. Renzo owns a company that makes specialized big screen TVs. From 2000 through 2015, the number of TVs produced can be modeled by M(x)= 3x^2-11x+20 where x is number of years since 2000. The average revenue per TV(in dollars) can be modeled by R(x)=60x+10. Write a polynomial T(x) that can be used to model Mr. Renzo's total revenue

T(x) = 180x³ - 630x² + 1090x + 200

Step-by-step explanation:

Total revenue = M(x) . R(x)

∵ M(x) = 3x² - 11x + 20

∵ R(x) = 60x + 10

∴ Total revenue = (3x² - 11x + 20)(60x + 10)

∵ T(x) can be used to model Mr. Renzo's total revenue

∴ T(x) = (3x² - 11x + 20)(60x + 10)

Let us multiply each term in the 1st bracket by each term in the 2nd bracket, then add the like terms

(3x² - 11x + 20)(60x + 10) = 3x²(60x) + 3x²(10) + (-11x)(60x) + (-11x)(10) + 20(60x) + 20(10)

(3x² - 11x + 20)(60x + 10) = 180x³ + 30x² + (-660x²) + (-110x) + 1200x + 200

Remember (-)(+) = (-)

(3x² - 11x + 20)(60x + 10) = 180x³ + 30x² - 660x² - 110x + 1200x + 200

Add like terms

(3x² - 11x + 20)(60x + 10) = 180x³ + (30x² - 660x²) + (-110x + 1200x) + 200

(3x² - 11x + 20)(60x + 10) = 180x³ - 630x² + 1090x + 200

∵ (3x² - 11x + 20)(60x + 10) = 180x³ - 630x² + 1090x + 200

∵ T(x) = (3x² - 11x + 20)(60x + 10)

∴ T(x) = 180x³ - 630x² + 1090x + 200

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