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