Find the number of polynomials \(P(x)\) of degree 4, with real coefficients, that satisfy \(P(x^2) = P(x) P(-x).\)
Looks like 10
\(\left( \begin{array}{c} x^4-x \\ x^4-3 x^3+3 x^2-x \\ x^4-x^3 \\ x^4 \\ x^4-2 x^3+x^2 \\ x^4+x^3+x^2 \\ x^4-4 x^3+6 x^2-4 x+1 \\ x^4-x^3-x+1 \\ x^4+x^3+x^2+x+1 \\ x^4+2 x^3+3 x^2+2 x+1 \\ \end{array} \right)\)
