Factor x^3 + 5x^2 + x + 5

Step by step

The question

Question: factor x³ + 5x² + x + 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 x².

From the second pair we take out 1.

Nothing else is common, so it is just 1.

Both leave the same bracket, x + 5.

Now both parts have x + 5 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 + 5 is in both parts, so we take it out once.

What is left, x² + 1, goes in the other bracket.

So we get (x + 5)(x² + 1).

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 + 5x² + x + 5 again.

So the answer is right!

Let's look back.

First: group in pairs.

Then: same bracket out.

Last: check.