Factor x^2 + 9

Step by step

The question

Question: factor completely x² + 9.

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

1 Common factor first

Always ask this first.

Here no number and no x goes into every term.

So there is no common factor.

2 Count the terms

The bracket has 2 terms.

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

3 Prime or not

x² + 9 is a square PLUS a square.

A sum of two squares does not factor.

We call it prime.

So x² + 9 is prime.

Careful!

(x + 3)² multiplied out has a middle term.

A sum of squares is prime.

Let's look back.

First: common factor first.

Then: count the terms.

Last: prime or not.