How do I find k if x^4-kx^3-2x^2+x+4 is divided by x-3 and the remainder is 16

If  x^4-kx^3-2x^2+x+4 is divide by x-3 , we get a
remainder 16, then

x^3-kx^3-2x^2+x+4-16 =  x^4-kx^3-2x^2+x
-12  is perfectly divisible by x-3.

We actually divide
:

x-3) x^4-kx^3-2x^2 +x -12(
x^3

x^4
-3x^3

----------------------

x-3)
 (-k+3)x^3 -2x^2( (-k+3)x^2

(-k+3)x^3  -
3(-k+3)x^2

-----------------------------------------------

x-3) (-3k
+7)x^2 + x (
((-3k+7)x

(-3k+7)x^2 -3(-3k+7)x

-----------------------------------------------------------

x-3)
(-9k +22)x  -12  ( (-9k+22)

(-9k +22)x -3
( -9k  +22)

-----------------------------------------------

0

Therefore -12
+3(-9k+22) = 0

-27k + 54 =
0.

-27k = -54.

k = -54/-27 =
2

or k = 2.

Therefore k = 2
for which x^4-kx^3 -2x^2+x+4 diveided by x-3 gives a remainder of
16.