Factor 2x^3 - 8x^2 - 6x + 24

Step by step

The question

Question: factor 2x³ − 8x² − 6x + 24.

There are four terms.

So we factor them in pairs.

This is called grouping.

1 Take out the common factor

All four terms can be divided by 2.

So we take 2 out first, like in the common factor lesson.

So it is 2(x³ − 4x² − 3x + 12).

Now we group what is in the bracket.

2 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.

3 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 2(x − 4)(x² − 3).

4 Check

Let's check: we multiply it back out.

Each part of the first bracket times each part of the second.

Then 2 times every term.

We get 2x³ − 8x² − 6x + 24 again.

So the answer is right!

Let's look back.

First: take out the common factor.

Then: group in pairs.

Then: same bracket out.

Last: check.