You want to take out as much as you can from that equation, but you can't take out more than the equation consists of.
Let's start with the 6.
6 is the most we can take out of the original equation, and still have integers left for coefficients.
Note that the smallest we have in the original equation is to the degree 1, se we need to take out an x of degree 1.
For the (your source of confusion)
Remember what i said in the beginning, take out as much as you can, but not more than there is in the equation.
So we have
The most we can take out there is a . If we, for instance, take out , our will become which only leaves us with a bigger mess.
If we only take out , we are also just keeping things complicated. Why only take the , when you can remove more from the equation to make it even simpler?
We cannot remove anything more than a to degree 1 from the equation. (Technically we can, but that doesn't mean we should )