Factor 2x^3 - 18x = 0

Step by step

The question

Question: solve 2x³ − 18x = 0.

The right side is 0 already.

1 Factor completely

Common factor first.

Every term has x, and every number divides by 2.

So we take out 2x.

So it is 2x(x² − 9) = 0.

Careful!

Don't divide both sides by x.

Then the answer x = 0 would be lost.

x² − 9 is one square take away another square.

x² is x squared.

9 is 3 squared.

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

So it is 2x(x + 3)(x − 3) = 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.

2 is a plain number.

It is never 0, so it does not make the product 0.

Each factor with x gives a small equation.

x = 0 is done already.

In x + 3 = 0, we take away 3 on both sides.

In x − 3 = 0, we add 3 on both sides.

So x = 0, x = −3 and x = 3.

Three answers.

3 Check

Let's check: put each answer into 2x³ − 18x = 0.

First x = 0.

Now x = −3.

Now x = 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.