Find the number of polynomials $P(x)$ of degree 4, with real coefficients, that satisfy
\[P(x^2) = P(x) P(-x).\]
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<|im_start|>user
Find the number of polynomials $P(x)$ of degree 4, with real coefficients, that satisfy
\[P(x^2) = P(x) P(-x).\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
10
Find the number of polynomials $P(x)$ of degree 4, with real coefficients, that satisfy
\[P(x^2) = P(x) P(-x).\]
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