x8+14x4+1
= x8+2x4+1+12x2
= ( x4+1)2+12x2
= (x4+1)2+ 4x2(x4+1) - 4x2(x4+1) +4x4+8x4
= (x4+1)2+ 4x2(x4+1) + 4x4 - 4x2(x4+1)+8x4
= (x4+1+2x2)2-4x2(x4+1-2x2)
= ( x4+1+2x2)2-4x2(x2-1)2
= ( x4+1+2x2)2 - (2x3-2x)2
= (x4+2x3+2x2-2x+1)(x4-2x3+2x2+2x+1)