Factor x^3 + x^2 - 7x - 7

Step by step

The question

Question: factor x³ + x² − 7x − 7.

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 −7, with the minus.

Both leave the same bracket, x + 1.

Careful!

If we take out 7, without the minus, we get −x − 1 in the bracket.

That does not match x + 1.

Take the minus out too.

Now both parts have x + 1 in them.

2 Same bracket out

x + 1 is in both parts, so we take it out once.

What is left, x² − 7, goes in the other bracket.

So we get (x + 1)(x² − 7).

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 + x² − 7x − 7 again.

So the answer is right!

Let's look back.

First: group in pairs.

Then: same bracket out.

Last: check.