We can do long division on this:
x−2x−2−x4−4x3−9x2−7x−7)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−x4−4x3−9x2−7x−7
We multiply x by −x3 to get to −x4, and so we have:
x−2x−2−x400−x3−9x2−7x−7)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−x4−4x3−9x2−7x−7
x−2x−2(−x4+2x3−9x2−7x−7¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0x4−6x3−9x2−7x−7)
We multiply x by −6x2 to get to −6x3 and so we have:
x−2x−2−x400−x3−6x2−7x−7)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−x4−4x3−9x2−7x−7
x−2x−2(−x4+2x3−9x2−7x−7¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0x4−6x3−9x2−7x−7)
x−2x−2(−x4−6x3+12x2−7x−7¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0x4−0x3−21x2−7x−7)
We multiply x by −21x to get to −21x2 and so we have:
x−2x−2−x400−x3−6x2−21x−7)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−x4−4x3−9x2−7x−7
x−2x−2(−x4+2x3−9x2−7x−7¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0x4−6x3−9x2−7x−7)
x−2x−2(−x4−6x3+12x2−7x−7¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0x4−0x3−21x2−7x−7)
x−2x−2(−x4−2x3−21x2+42x−7¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0x4−0x3−0x2−49x−7)
We multiply x by −49 to get to −49x and so we have:
x−2x−2−x400−x3−6x2−21x−49)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−x4−4x3−9x2−7x−7
x−2x−2(−x4+2x3−9x2−7x−7¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0x4−6x3−9x2−7x−7)
x−2x−2(−x4−6x3+12x2−7x−7¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0x4−0x3−21x2−7x−7)
x−2x−2(−x4−2x3−21x2+42x−7¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0x4−0x3−0x2−49x−7)
x−2x−2(−x4−2x3−1x2−49x+98¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0x4−0x3−0x2−0x−105)
And so −x4−43−9x2−7x−7x−2=−x3−6x2−21x−49 with a remainder of −105
