Factor 3x^3 + 6x^2 + 9x + 18

Step by step

The question

Question: factor 3x³ + 6x² + 9x + 18.

There are four terms.

So we factor them in pairs.

This is called grouping.

1 Take out the common factor

All four terms can be divided by 3.

So we take 3 out first, like in the common factor lesson.

So it is 3(x³ + 2x² + 3x + 6).

Now we group what is in the bracket.

2 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 3.

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.

3 Same bracket out

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

What is left, x² + 3, goes in the other bracket.

So we get 3(x + 2)(x² + 3).

4 Check

Let's check: we multiply it back out.

Each part of the first bracket times each part of the second.

Then 3 times every term.

We get 3x³ + 6x² + 9x + 18 again.

So the answer is right!

Let's look back.

First: take out the common factor.

Then: group in pairs.

Then: same bracket out.

Last: check.