Step by step
The question
Question: factor x³ − 3x² − 2x + 6.
There are four terms.
So we factor them in pairs.
This is called grouping.
1 Group in pairs
We put the first two together, and the last two together.
From the first pair we take out x².
The second pair starts with a minus.
So we take out −2, with the minus.
Both leave the same bracket, x − 3.
Careful!
If we take out 2, without the minus, we get −x + 3 in the bracket.
That does not match x − 3.
Take the minus out too.
Now both parts have x − 3 in them.
2 Same bracket out
x − 3 is in both parts, so we take it out once.
What is left, x² − 2, goes in the other bracket.
So we get (x − 3)(x² − 2).
3 Check
Let's check: we multiply it back out.
Each part of the first bracket times each part of the second.
We get x³ − 3x² − 2x + 6 again.
So the answer is right!
Let's look back.
First: group in pairs.
Then: same bracket out.
Last: check.