Factor 4x^3 = 36x Step by Step | Solving by factoring

Step by step

The question

Question: solve 4x³ = 36x.

4x³ = 36x

1 Get 0 on one side

To factor, we want 0 on the right side.

So we take away 36x on both sides.

We do it on both sides, so they stay equal.

4x³ − 36x = 36x − 36x

Now we have 4x³ − 36x = 0.

4x³ − 36x = 0

2 Factor completely

Common factor first.

Every term has x, and every number divides by 4.

So we take out 4x.

common factor: 4x

So it is 4x(x² − 9) = 0.

4x(x² − 9) = 0

Careful!

Don't divide both sides by x.

Then the answer x = 0 would be lost.

Careful: don't divide by x. We would lose x = 0.

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.

a² − b² = (a + b)(a − b)

x² = (x)², 9 = 3²

So it is 4x(x + 3)(x − 3) = 0.

4x(x + 3)(x − 3) = 0

3 Each factor is 0

Some numbers multiply to 0.

That only happens if one of them is 0.

So we make each factor 0.

A × B × C = 0 → A = 0 or B = 0 or C = 0

4 is a plain number.

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

4 ≠ 0

Each factor with x gives a small equation.

x = 0 or x + 3 = 0 or x − 3 = 0

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.

x = 0 or x = −3 or x = 3

So x = 0, x = −3 and x = 3.

Three answers.

4 Check

Let's check: put each answer into 4x³ − 36x = 0.

First x = 0.

x = 0: 4(0)³ − 36(0) = 0 + 0 = 0

Now x = −3.

x = −3: 4(−3)³ − 36(−3) = −108 + 108 = 0

Now x = 3.

x = 3: 4(3)³ − 36(3) = 108 − 108 = 0

We get 0 every time.

So all three answers are right!

Let's look back.

First: get 0 on one side.

Then: factor completely.

Then: each factor is 0.

Last: check.

Answer