A polynomial $P$ is given. \[ P(x)=x^{4}+64 x^{2} \] (a) Find all zeros of $P$, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) \[ x= \] (b) Factor $P$ completely. \[ P(x)= \]

Step 1 ：Given the polynomial \(P(x) = x^{4} + 64x^{2}\).

Step 2 ：First, we find the zeros of the polynomial by setting \(P(x) = 0\) and solving for \(x\).

Step 3 ：Solving the equation gives us the zeros of the polynomial as \(x = 0, -8i, 8i\).

Step 4 ：Next, we factor the polynomial completely using the zeros we found.

Step 5 ：Factoring the polynomial gives us \(P(x) = x^{2}(x^{2} + 64)\).

Step 6 ：\(\boxed{\text{The zeros of the polynomial are } x = 0, -8i, 8i \text{ and the factored form of the polynomial is } P(x) = x^{2}(x^{2} + 64)}\)