Polynomial is 2(x-4)4(x+2).
(a+b)4=a4+4a3b+6a2b2+4ab3+b4; let a=x and b=-4:
(x-4)4=x4-16x3+96x2-256x+256.
(x+2)(x-4)4=x(x-4)4+2(x-4)4=
x5-16x4+96x3-256x2+256x
+2x4-32x3+192x2-512x+512=
x5-14x4+64x3-64x2-256x+512.
Polynomial is:
2x5-28x4+128x3-128x2-512x+1024.