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.
From the second pair we take out 2.
Both leave the same bracket, x + 3.
Now both parts have x + 3 in them.
Careful!
This is not the answer yet.
It is still two parts added.
Factored means one thing times another.
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.