Question

Answer question (picture below) and show work please

Answer 1

`A(x)=7x^2-2x+10`

Explanation:

Long Division

The polynomial long division implies the sequential division of each term of the dividend polynomial by the terms of the divisor polynomial. The procedure is a well-know sequence of steps from which there are two outputs: the quotient and the remainder.

We have two mathematical models, one for the total number of visitors who went to a theme park:

`F(x)=126x^3+279x^2+90x+450`

The other for the number of shows played at the theme park in the same period

`G(x)=18x+45`

Where x is the number of days since October 1. We are required to find the expression for the average number of visitors per show. It comes by dividing F(x) by G(x). We must perform a long division as shown below.

The average number of visitors per show is

`A(x)=7x^2-2x+10`

For example, day 5

`A(5)=7\ 5^2-2(5)+10=175`

There were 175 visitors per show (on average)