Step by step
The question
Question: factor x³ + 4x² − 3x − 12.
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 −3, with the minus.
Both leave the same bracket, x + 4.
Careful!
If we take out 3, without the minus, we get −x − 4 in the bracket.
That does not match x + 4.
Take the minus out too.
Now both parts have x + 4 in them.
2 Same bracket out
x + 4 is in both parts, so we take it out once.
What is left, x² − 3, goes in the other bracket.
So we get (x + 4)(x² − 3).
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 + 4x² − 3x − 12 again.
So the answer is right!
Let's look back.
First: group in pairs.
Then: same bracket out.
Last: check.