```Question 119638
I assume you mean:

(4x^4 - 12x^3 - 48x - 60) / (x - 4)

The most straight forward way is to solve this long division style. We will use 0x^2 as a place holder. As follows:

:::::::::::::::::4*x^3 +  4*x^2 + 16*x + 16 + 4/(x-4)
_____________________________________
(x-4) | 4*x^4 - 12*x^3 -  0*x^2 - 48*x - 60
::::::-(4*x^4 - 16*x^3)
::::::________________
:::::::::::0     4*x^3 -  0*x^2
:::::::::::::::-(4*x^3 - 16*x^2)
:::::::::::::::________________
:::::::::::::::::::0     16*x^2 - 48*x
:::::::::::::::::::::::-(16*x^2 - 64*x)
:::::::::::::::::::::::_______________
:::::::::::::::::::::::::::0      16*x - 60
::::::::::::::::::::::::::::::::-(16*x - 64)
::::::::::::::::::::::::::::::::___________
::::::::::::::::::::::::::::::::::::::::::4

Factor 4 out from: 4x^3 + 4x^2 + 16x + 16 + 4/(x-4)

4*(x^3 + x^2 + 4x + 4 + 1/(x-4))

Check:

1. (x-4)*4*(x^3 + x^2 + 4*x + 4 + 1/(x-4)) Multiply 4 into (x^3...)
2. (x-4) * (4*x^3 + 4*x^2 + 16*x + 16 + 4/(x-4)) Multiply (x-4) into (4*x^3...)
3. 4*x^4 - 16*x^3 + 4x^3 - 16*x^2 + 16*x^2 - 64*x + 16*x - 64 + 4 Simplify
4. 4*x^4 - 12*x^3 - 48*x - 60```