What is the purpose of division of polynomials?

Answer 1

Mainly, sometimes to solve real-world problems, you have to divide polynomials.
It helps if you know how to do it.

Some examples are:

Calculating power across speakers on an amplifier (I had a roommate who blew up my woofers one time!)

The first widget costs $10, but the rest cost $5. Find the average cost of a bunch of widgets.

Or, how about figuring what score you need on the next test to get a passing grade?!?