The total yield of corn on Mr. Geller's farm from 1991 to 2010 can be modeled by the function F (x) = 2x3+144x2-486x-2700 (measured in kilograms) and the area of Mr. Geller's farm from 1991 to 2010 can be modeled by G (x) = 2x + 150 (measured in hectares), where x is the number of years since1991. a. What is the average yield of corn per hectare?

x2 - 3x - 18

Step-by-step explanation:

To find the average yield of corn per hectare we just need to divide the function F (x) by the function G (x).

First we need to divide the higher term of F (x) (2x3) by the higher term of G (x) (2x), then we have 2x3 / 2x = x2 (first part of the final result)

Multiplying x2 by G (x), we have 2x3 + 150x2

Subtracting this result from F (x), we have - 6x2 - 486x - 2700

Dividing the higher term of the result (-6x2) by 2x again, we have - 3x (second part of the final result)

Multiplying - 3x by G (x), we have - 6x2 - 450x

Subtracting this result from - 6x2 - 486x - 2700, we have - 36x - 2700

Dividing the higher term of the result (-36x) by 2x again, we have - 18 (last part of the final result)

Multiplying - 18 by G (x), we have - 36x - 2700

Subtracting this result from - 36x - 2700, we have 0

So the resulting polynomial that represents the average yield of corn per hectare is x2 - 3x - 18