(x²+x+1)（x²-6x+1)+12x²
＝(x^2+1)^2-5x(x^2+1)-6x^2+12x^2
=(x^2+1)^2-5x(x^2+1)+6x^2
=(x^2－2x+1)（x²-3x+1)
=(x-1)^2(x^2-3x+1)