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