Question

4x^4-8x^3+12x^2-6x+12/2x+4 with polynomial long division

Answer 1

Use synthetic division, it's easier:
2x+4 intersects x axis at -2.

coefficients of the quartic expression are:
4 -8 12 -6 12

using synthetic division:
4 -16 44 -94 200

answer:
4x^3 - 16x^2 + 44x -94 + (100/(x+2))