Factor completely x^3 + 4x

Step by step

The question

Question: factor completely x³ + 4x.

Completely means: until no part can be factored any more.

1 Common factor first

Every term has x.

So the common factor is x.

We divide every term by it.

What is left goes in the bracket.

So it is x(x² + 4).

2 Count the terms

The bracket has 2 terms.

With 2 terms we look for two squares or two cubes.

3 Check each bracket

x² + 4 is a square PLUS a square.

A sum of two squares does not factor.

We call it prime.

No bracket can be factored any more.

So we are done.

Careful!

Many people stop after taking out the common factor.

Always check if the bracket factors too.

4 Check

Let's check: we multiply it back out.

We get x³ + 4x again.

So it is right!

Let's look back.

First: common factor first.

Then: count the terms.

Then: check each bracket.

Last: check.