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6\left(5z^{4}+z^{3}+z\right)
Factor out 6.
z\left(5z^{3}+z^{2}+1\right)
Consider 5z^{4}+z^{3}+z. Factor out z.
6z\left(5z^{3}+z^{2}+1\right)
Rewrite the complete factored expression. Polynomial 5z^{3}+z^{2}+1 is not factored since it does not have any rational roots.