x²-x=-1
x²-x+1=0
3x^4-5x³+8x²-5x+1 = (3x^4-3x³+3x²)+(-2x³+2x²-2x)+(3x²-3x+3)-2
= 3x²(x²-x+1)-2x(x²-x+1)+3(x²-x+1)-2 = -2