<em><u>The polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck is:</u></em>
![f(x) = -0.04x^2 + 18x + 75](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20-0.04x%5E2%20%2B%2018x%20%2B%2075)
<em><u>Solution:</u></em>
<em><u>The cost of distributing by train can be modeled as:</u></em>
![-0.07x^2 + 40x - 105](https://tex.z-dn.net/?f=-0.07x%5E2%20%2B%2040x%20-%20105)
<em><u>The cost of distributing by truck can be modeled as:</u></em>
![-0.03x^2 + 22x - 180](https://tex.z-dn.net/?f=-0.03x%5E2%20%2B%2022x%20-%20180)
where x is the number of tons of product distributed
To find: Difference between the cost of distributing by train and the cost of distributing by truck
Difference = cost of distributing by train - cost of distributing by truck
Let f(x) = difference in cost between trains & trucks
![f(x) = (-0.07x^2+40x-105) - (-0.03x^2 +22x - 180)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28-0.07x%5E2%2B40x-105%29%20-%20%28-0.03x%5E2%20%2B22x%20-%20180%29)
![f(x) = -0.07x^2 + 40x -105 + 0.03x^2 -22x + 180](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-0.07x%5E2%20%2B%2040x%20-105%20%2B%200.03x%5E2%20-22x%20%2B%20180)
![Combine\ the\ like\ terms\\\\f(x) = -0.07x^2 +0.03x^2 + 40x - 22x +180-105\\\\Add\ the\ like\ terms\\\\f(x) = -0.04x^2 + 18x + 75](https://tex.z-dn.net/?f=Combine%5C%20the%5C%20like%5C%20terms%5C%5C%5C%5Cf%28x%29%20%3D%20-0.07x%5E2%20%2B0.03x%5E2%20%2B%2040x%20-%2022x%20%2B180-105%5C%5C%5C%5CAdd%5C%20the%5C%20like%5C%20terms%5C%5C%5C%5Cf%28x%29%20%3D%20%20-0.04x%5E2%20%2B%2018x%20%2B%2075)
Thus polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck is found