as x+6 is the quotient, you need to use -6
-6 | 4 -3 +5 6
x -24 +162 -1002
add
4 -27 167 -996
f(x)= 4x^2 -27x +167 - 996/(x+6)
Lets check
(x+6)(4x^2 -27x +167)= 4x^3 -27x^2 +167x + 24x^2 - 162x + 1002 =
= 4x^3 - 3x^2 +5x +1002
1002-996= 6
So we have the correct solution: 4x^2 -27x +167 - 996/(x+6)