Question 933067
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Hi
x-2 is a factor of x^3-x^2+kx-2.
2	1	-1	k	-2
		2	2	2k+4
	1	1	k+ 2	0
				k = -1  {{{2k+4 = 2}}}
.........
x-4 is a factor of x^3-k^2x^2-8kx-16
4	1	-k^2	  -8k	      -16
		4	16 - 4k^2	      -16k^2 - 32k + 64
	1	4-k^2	-4k^2 - 8k + 16	      0
				            k = -3,1  {{{-16k^2 - 32k + 64 = 16}}}
Synthetic Division works well here.