Step by step
The question
Question: solve x³ − 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(x² − 4) = 0.
Careful!
Don't divide both sides by x.
Then the answer x = 0 would be lost.
x² − 4 is one square take away another square.
x² is x squared.
4 is 2 squared.
A square minus a square is the plus bracket times the minus bracket.
So it is x(x + 2)(x − 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 x + 2 = 0, we take away 2 on both sides.
In x − 2 = 0, we add 2 on both sides.
So x = 0, x = −2 and x = 2.
Three answers.
3 Check
Let's check: put each answer into x³ − 4x = 0.
First x = 0.
Now x = −2.
Now x = 2.
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.