Factor 9x^3 - 4x = 0

Step by step

The question

Question: solve 9x³ − 4x = 0.

The right side is 0 already.

1 Factor completely

Common factor first.

Every term has x.

So we take out x.

So it is x(9x² − 4) = 0.

Careful!

Don't divide both sides by x.

Then the answer x = 0 would be lost.

9x² − 4 is one square take away another square.

9x² is 3x squared.

4 is 2 squared.

A square minus a square is the plus bracket times the minus bracket.

So it is x(3x + 2)(3x − 2) = 0.

2 Each factor is 0

Some numbers multiply to 0.

That only happens if one of them is 0.

So we make each factor 0.

Each factor with x gives a small equation.

x = 0 is done already.

In 3x + 2 = 0, we take away 2 on both sides, then divide by 3.

In 3x − 2 = 0, we add 2 on both sides, then divide by 3.

So x = 0, x = −2/3 and x = 2/3.

Three answers.

3 Check

Let's check: put each answer into 9x³ − 4x = 0.

First x = 0.

Now x = −2/3.

Now x = 2/3.

We get 0 every time.

So all three answers are right!

Let's look back.

First: factor completely.

Then: each factor is 0.

Last: check.