Solve the Equation x⁴ - 8x = 0: Finding All Solutions

To solve the equation $x^4 - 8x = 0$, we'll follow these steps:

• Step 1: Factor out the greatest common factor.
• Step 2: Set each factor equal to zero and solve for $x$.

Now, let's work through each step:
Step 1: The equation given is $x^4 - 8x = 0$. Both terms on the left contain $x$ as a factor. We can factor out $x$ to rewrite the equation as:

$x(x^3 - 8) = 0$

Step 2: To find the solutions, set each factor to zero.

If $x = 0$, then one solution is:

$x = 0$

Next, solve for $x$ in the equation $x^3 - 8 = 0$:
Add 8 to both sides:

$x^3 = 8$

Take the cube root of both sides:

$x = \sqrt[3]{8} = 2$

Therefore, the solutions to the equation $x^4 - 8x = 0$ are $x = 0$ and $x = 2$.

Thus, the correct answer is: $x = 0, 2$.