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t^{2}\left(t-5\right)-2\left(t-5\right)
Do the grouping t^{3}-5t^{2}+10-2t=\left(t^{3}-5t^{2}\right)+\left(10-2t\right), and factor out t^{2} in the first and -2 in the second group.
\left(t-5\right)\left(t^{2}-2\right)
Factor out common term t-5 by using distributive property. Polynomial t^{2}-2 is not factored since it does not have any rational roots.