We will have that the value of k is the following:
Coefficients are: 3, k, & -1
And we will have x = -4
So:
-4 | 3 k -1
| -12 (-4k + 48)
------------------------------------
3 (k - 12) (-4k + 47)
Operation steps:
// -4(4) = -12
// k - 12
// -4(k -12) = -4k +48
//-1 +(-4k + 48) = -4k +47
So, we have that the remainder is -4k + 47, now we replace with the known value of the remainder: 27:
-4k + 47 = 27 => -4k = -20 => k = 5
So, the value of k is 5.