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Let's solve the given polynomial equation step by step.

### Given Equation:
\[ 2x^4 - 72x^2 = 0 \]

### Step 1: Factor the equation
First, let's factor out the greatest common factor (GCF). In this case, the GCF is \( 2x^2 \):

\[ 2x^2(x^2 - 36) = 0 \]

### Step 2: Solve each factor separately
Now that we have factored the equation, we can set each factor equal to zero and solve.

#### Factor 1: \( 2x^2 = 0 \)
\[ x^2 = 0 \]
Taking the square root of both sides:
\[ x = 0 \]

#### Factor 2: \( x^2 - 36 = 0 \)
\[ x^2 = 36 \]
Taking the square root of both sides:
\[ x = \pm 6 \]

### Step 3: Identify all solutions
The solutions to the equation are:
\[ x = 0, \, x = 6, \, x = -6 \]

### Step 4: Answer the question
The equation in factored form is:
\[ 2x^2(x - 6)(x + 6) = 0 \]

So, the correct solution would be to factor the equation as:
\[ 2x^2(x - 6)(x + 6) = 0 \]
and the solutions are \( x = 0 \), \( x = 6 \), and \( x = -6 \).

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Solve the equation \( x^4 - 16x^2 = 0 \).
2. Factor and solve \( 3x^4 - 27x^2 = 0 \).
3. Solve the quadratic equation \( x^2 - 49 = 0 \).
4. Factor \( 4x^4 - 64x^2 = 0 \) and find the solutions.
5. Solve \( x^2(x - 4)(x + 4) = 0 \) and list all roots.

**Tip:** Always factor out the greatest common factor first when solving polynomial equations. It simplifies the equation and makes it easier to solve.

Learn how to factor and solve the polynomial equation 2x^4 - 72x^2 = 0 with a detailed step-by-step solution. This problem covers polynomial equations, factoring techniques, and quadratic equations. Suitable for students in Grades 9-12.

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