Factor x^3 - 2x^2 + 5x - 10

Step by step

The question

Question: factor x³ − 2x² + 5x − 10.

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 − 2.

Now both parts have x − 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

x − 2 is in both parts, so we take it out once.

What is left, x² + 5, goes in the other bracket.

So we get (x − 2)(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 − 2x² + 5x − 10 again.

So the answer is right!

Let's look back.

First: group in pairs.

Then: same bracket out.

Last: check.