Question

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?

Answer 1

x2 - 3x - 18

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