We are asked to solve the equation:

\[
0 = 4x^3 - 8x
\]

### Step 1: Factor the equation

We can factor out the greatest common factor, which is \( 4x \):

\[
0 = 4x(x^2 - 2)
\]

### Step 2: Set each factor to zero

Now, set each factor equal to zero:

1. \( 4x = 0 \)
2. \( x^2 - 2 = 0 \)

### Step 3: Solve each equation

1. \( 4x = 0 \) implies \( x = 0 \).
2. \( x^2 - 2 = 0 \) implies \( x^2 = 2 \), so \( x = \pm \sqrt{2} \).

### Final Solution:

The solutions are:

\[
x = 0, \, x = \sqrt{2}, \, x = -\sqrt{2}
\]

Would you like a more detailed explanation of any step?

Here are 5 related questions:
1. How do you factor more complex cubic equations?
2. What is the general method for solving quadratic equations?
3. Can we apply the quadratic formula to solve \(x^2 - 2 = 0\)?
4. What are the differences between real and complex roots in equations?
5. How do you graph the function \( 4x^3 - 8x \) and find its roots?

**Tip**: When solving polynomial equations, always check if factoring can simplify the process before trying other methods like the quadratic formula.

Learn how to solve the cubic equation 0 = 4x^3 - 8x by factoring and using the quadratic equation. This solution provides a detailed step-by-step breakdown, involving factoring and solving for real roots, suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation