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4\left(k^{3}-1\right)
Factor out 4.
\left(k-1\right)\left(k^{2}+k+1\right)
Consider k^{3}-1. Rewrite k^{3}-1 as k^{3}-1^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).
4\left(k-1\right)\left(k^{2}+k+1\right)
Rewrite the complete factored expression. Polynomial k^{2}+k+1 is not factored since it does not have any rational roots.