Q:  Factor by Grouping:  -4q³u-2q²u-4qu

A:  Normally we “factor by grouping” where there are 4 different terms… Our problem only has three terms, but that is no matter.  We can still do it!

Start with our problem:

-4q³u-2q²u-4qu

Now I am going to group it like so:

(-4q³u – 2q²u) – (4qu)

Since I see a “4qu” in the back, that is what I am going to factor out of the front, like so:

4qu(-q² – ½q) – 1(4qu)

So, now I can pull a “4qu” out of the first group and out of the second group:

4qu [ -q² – ½q – 1 ]

I have now factored that thing by group.  It was not my favorite method for this problem, but it worked.