怎么将x^4 - (x1+x2)x^3 + (x1*x2-2)x^2 - (x1+x2)x +1因式分解?分解成（x^2 - x1*x - 1）* (x^2 - x2 -1)

题目

怎么将x^4 - (x1+x2)x^3 + (x1*x2-2)x^2 - (x1+x2)x +1因式分解?分解成（x^2 - x1*x - 1）* (x^2 - x2 -1)

答案

x^4 - (x1+x2)x^3 + (x1*x2 - 2)x^2 + (x1 + x2)x +1= x^4 - x1*x^3 - x2*x^3 + x1*x2*x^2- 2x^2 + x1x + x2x + 1= (x^4 - x2*x^3 - x^2)+ (- x1*x^3+ x1*x2x^2 + x1*x)+ (- x^2 + x2*x + 1)= x^2(x^2 - x2*x - 1)- ...