Part 1 of 2
Use factoring and the root method to solve the polynomial equation.
\[
5 x^{4}-25 x^{2}=0
\]
Rewrite the equation in a completely factored form.
\[
\square=0
\]
(Type your answer in factored form. Use integers or fractions for any numbers in the expression.)
Answer
Final Answer: The factored form of the equation is \(\boxed{5x^2(x^2 - 5) = 0}\).
Step 1 ：First, we factor out the common terms from the equation \(5x^{4}-25x^{2}=0\). In this case, we can factor out \(5x^2\) from both terms.
Step 2 ：By factoring, we rewrite the equation in a completely factored form as \(5x^2(x^2 - 5) = 0\).
Step 3 ：We then use the zero product property to find the roots of the equation. The zero product property states that if the product of multiple factors is zero, then at least one of the factors must be zero.
Step 4 ：This occurs when \(5x^2 = 0\) or when \(x^2 - 5 = 0\).
Step 5 ：Final Answer: The factored form of the equation is \(\boxed{5x^2(x^2 - 5) = 0}\).
