Step by step
The question
Question: factor 3xy + 6x + 2y + 4.
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 3x.
From the second pair we take out 2.
Both leave the same bracket, y + 2.
Now both parts have y + 2 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
y + 2 is in both parts, so we take it out once.
What is left, 3x + 2, goes in the other bracket.
So we get (y + 2)(3x + 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 3xy + 6x + 2y + 4 again.
So the answer is right!
Let's look back.
First: group in pairs.
Then: same bracket out.
Last: check.