1. ## Advanced Functions: Solving Polynomial Equations Word Problem

Here's the problem fellas: Between 1985 through 1995, the number of home computers, in thousands, sold in Canada is estimated by this equation where t is in years and t=0 for 1985. $\displaystyle C(t)=0.92(t^3+8t^2+40t+400)$ In what year did home computer sales reach 1.5 million?

Well here's what I've got down so far.
Since it's expressed in thousands 1.5 million is expressed as 1500.

$\displaystyle 1500=0.92(t^3+8t^2+40t+400)$
$\displaystyle 1500=0.92t^3+7.36t^2+36.8t+368$
$\displaystyle 0=0.92t^3+7.36t^2+36.8t+368-1500$
$\displaystyle 0=0.92t^3+7.36t^2+36.8t-1132$

Now I think I'm supposed to factor it to get the answer, but I've tried the factor theorem with no result. By graphing the answer is 7.67 years, but we have to solve it algebraically. In the back of the book, the answer is 8 years.

How would you solve this?

There is one real root of this equation x = 7.67526
Solve by graphing utility/calculator. There are no factors.

So, x = 8

3. Just as I thought, but for some reason we are explicitly supposed to solve it algebraically.

Thank you.