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2z^{2}+8+10z^{3}-12
Combine -2z^{2} and 4z^{2} to get 2z^{2}.
2z^{2}-4+10z^{3}
Subtract 12 from 8 to get -4.
2\left(z^{2}-2+5z^{3}\right)
Factor out 2. Polynomial 5z^{3}+z^{2}-2 is not factored since it does not have any rational roots.