Step by step
The question
Question: factor x³ + 4x² + 5x + 20.
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 5.
Both leave the same bracket, x + 4.
Now both parts have x + 4 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 + 4 is in both parts, so we take it out once.
What is left, x² + 5, goes in the other bracket.
So we get (x + 4)(x² + 5).
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 + 5x + 20 again.
So the answer is right!
Let's look back.
First: group in pairs.
Then: same bracket out.
Last: check.