Step by step
The question
Question: factor 6x³ − 3x² − 10x + 5.
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 3x².
The second pair starts with a minus.
So we take out −5, with the minus.
Both leave the same bracket, 2x − 1.
Careful!
If we take out 5, without the minus, we get −2x + 1 in the bracket.
That does not match 2x − 1.
Take the minus out too.
Now both parts have 2x − 1 in them.
2 Same bracket out
2x − 1 is in both parts, so we take it out once.
What is left, 3x² − 5, goes in the other bracket.
So we get (2x − 1)(3x² − 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 6x³ − 3x² − 10x + 5 again.
So the answer is right!
Let's look back.
First: group in pairs.
Then: same bracket out.
Last: check.