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