Question

y^2+y-2+(y-1)x+(y+2)x^2+x^3因式分解

Answer 1

=(y+2)×（y-1)+(y-1)x+x^2(y+2+x)
=(y-1)(y+2+x)+x^2(y+2+x)
=(y+2+x)(y-1+x^2)

Answer 2

观察发现x最高次为3，y最高次为2，未发现分数因子。设为（x^2+y+a)(x+y+b)
展开得x^3+x^2×(y+a)+x(y+b)+y^2+(a+b)y+ab
对照得ab=-2 a=2 b=-1
所以a=2 b=-1
y^2+y-2+(y-1)x+(y+2)x^2+x^3=(x+y+2)(x^2+y-1)