OrePolynomial[{{(-4 + x)*(-1 + x)^2*x*(4 - 6*x + x^2)*(4 + 3*x + x^2)*
    (768 - 1536*x + 1472*x^2 - 936*x^3 + 44*x^4 + 268*x^5 - 75*x^6 + 13*x^7), 
   {3}}, {3*(-1 + x)*(-16384 - 24576*x + 93184*x^2 - 32768*x^3 + 3072*x^4 - 
     64000*x^5 + 79040*x^6 - 73632*x^7 + 44056*x^8 - 3008*x^9 - 6483*x^10 + 
     2579*x^11 - 471*x^12 + 39*x^13), {2}}, 
  {6*(-24576 + 53248*x - 110080*x^2 + 212480*x^3 - 163328*x^4 - 32000*x^5 + 
     138304*x^6 - 116640*x^7 + 50784*x^8 - 3672*x^9 - 6482*x^10 + 2583*x^11 - 
     444*x^12 + 39*x^13), {1}}, 
  {6*(8192 - 20480*x + 35328*x^2 - 38912*x^3 + 14848*x^4 + 12800*x^5 - 
     20384*x^6 + 13152*x^7 - 3560*x^8 - 920*x^9 + 697*x^10 - 126*x^11 + 
     13*x^12), {0}}}, OreAlgebraObject[{Der[x]}, Factor, Factor[#1 + #2] & , 
  #1*#2 & , None], DegreeLexicographic]
