I have never known how to do these problems and there are plenty on the exam.
A rectangle has an area of (x^3-6x^2+10x-8) square meters and a width of (x-4) meters. What is its length?
How would I set this problem up???
If we just forget about the $\displaystyle x$ for a minute, I'm sure you know that the equation for the area of a rectangle is $\displaystyle A = w \times l$
Putting your above values into that question, we get the equation:
$\displaystyle x^3-6x^2+10x-8 = (x - 4)l$
Or $\displaystyle l = \frac{x^3-6x^2+10x-8}{x - 4}$
What we have now is just a simple polynomial division question.
There are several methods to solve this, I would suggest Synthetic Division, but use whatever method you have been taught.
Hope this helps