X^4-4x+3=X^4-1 -4x+4 =(x^2-1)(x^2+1)-4(x-1) =(x^2+1)(x+1)(x-1)-4(x-1) =(x-1)[(x^2+1)(x+1)-4]上结果中的因式,(x^2+1)(x+1)-4再因式分解可得：(x^2+1)(x+1)-4=x^3+x^2+x-3 ...