https://file.aiquickdraw.com/mathbot/file/1727475628347q1kc717q.jpg

The equation presented is:

\[
4x^4 - 36x^2 = 0
\]

To solve this equation using factoring, follow these steps:

### Step 1: Factor the common term
First, notice that both terms share a common factor of \( 4x^2 \). Factor it out:

\[
4x^2(x^2 - 9) = 0
\]

### Step 2: Apply the Zero Product Property
Now that the equation is factored, set each factor equal to zero.

1. \( 4x^2 = 0 \)
2. \( x^2 - 9 = 0 \)

### Step 3: Solve each equation
1. Solve \( 4x^2 = 0 \):
   \[
   x^2 = 0 \quad \Rightarrow \quad x = 0
   \]

2. Solve \( x^2 - 9 = 0 \):
   \[
   x^2 = 9 \quad \Rightarrow \quad x = \pm 3
   \]

### Final Solution Set
The solution set is:

\[
x = 0, \, x = 3, \, x = -3
\]

So, the solution set is \( \{ 0, 3, -3 \} \). Select option A, and enter the solution set as `0, 3, -3`.

Would you like more details on any of these steps?

### Related Questions:
1. How do you factor other types of polynomial equations?
2. What is the Zero Product Property, and how is it used?
3. How do you solve quadratic equations by factoring?
4. What are the solutions for equations with higher powers (e.g., cubic equations)?
5. How can graphing be used to check solutions for polynomial equations?

### Tip:
Always check the factored form by expanding it back to ensure it's correct before solving.

Use factoring to solve the polynomial equation: 4x^4 - 36x^2 = 0. Find the solution set.

Learn how to solve the polynomial equation 4x^4 - 36x^2 = 0 by factoring. This detailed step-by-step guide uses the Zero Product Property to find the solution set, covering important algebraic concepts. Suitable for students in Grades 9-12.

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