Question

How do you divide `(-x3 + 22x2 - 120x) div (x - 12)`?

Answer 1

Factoring allows you to divide easily to get `-x^2+10x`

Explanation:

First pull a `-x` out of `(-x^3+22x^2-120x)` to get:

`-x(x^2-22x+120)`

This can be factored to get

`-x(x-12)(x-10)`

The first thing i would look for when factoring is to see if what you are dividing by, in this case (x-12), is part of the factored form.
This makes solving very easy because they simply cancel out and you are left with `-x(x-10)=-x^2+10x`