A movie website offers one free movie viewing to anyone that registers. The total number of people that register can be modeled by the function f(x)=−27x3−135x2−72x+220, where x is the number of months passed since starting the website. The number of free movies available to choose from can be modeled as 3x+11. Write an expression that can be used to determine the average number of people that watch each free movie. Simplify your answer.

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

ιт ιѕ $222.95

step-by-step explanation:

αℓℓ уσυ gσт тσ ∂σ ιѕ fιgυяє συт ωнαт 30% σf $318.50 ιѕ $95.55

тнєи ѕυвтяα¢т ιт fяσм $318.50-$95.55=$222.95

нσρє ι ¢συℓ∂ нєℓρ уσυ συ