Simplifying
k4 + 2k3 + 3k2 + 4k

Reorder the terms:
4k + 3k2 + 2k3 + k4

Factor out the Greatest Common Factor (GCF), 'k'.
k(4 + 3k + 2k2 + k3)

Final result:
k(4 + 3k + 2k2 + k3)