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-6\left(-h+k\right)+h^{3}\left(-h+k\right)
Do the grouping 6h-6k-h^{4}+h^{3}k=\left(6h-6k\right)+\left(-h^{4}+h^{3}k\right), and factor out -6 in the first and h^{3} in the second group.
\left(-h+k\right)\left(-6+h^{3}\right)
Factor out common term -h+k by using distributive property. Polynomial h^{3}-6 is not factored since it does not have any rational roots.