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t^{2}\left(t-1\right)+t-1
Do the grouping t^{3}-t^{2}+t-1=\left(t^{3}-t^{2}\right)+\left(t-1\right), and factor out t^{2} in t^{3}-t^{2}.
\left(t-1\right)\left(t^{2}+1\right)
Factor out common term t-1 by using distributive property. Polynomial t^{2}+1 is not factored since it does not have any rational roots.