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4\left(z^{2}-2z-2z^{4}\right)
Factor out 4.
z\left(z-2-2z^{3}\right)
Consider z^{2}-2z-2z^{4}. Factor out z.
4z\left(z-2-2z^{3}\right)
Rewrite the complete factored expression. Polynomial z-2-2z^{3} is not factored since it does not have any rational roots.