x3-y3-x2+2xy-y2 因式分解还有：(2) x2+2xy-3y2+3x+y+2(3) 6x2-7x-4（实数范围内）
问题描述：
x3-y3-x2+2xy-y2 因式分解
还有：(2) x2+2xy-3y2+3x+y+2
(3) 6x2-7x-4（实数范围内）
答
1)x^3-y^3-x^2+2xy-y^2
=x^3-y^3-(x^2-2xy+y^2)
=(x-y)(x^2+xy+y^2)-(x-y)^2
=(x-y)(x^2+xy+y^2-x+y)
2)x^2+2xy-3y^2+3x+y+2
=(x+3y)(x-y)+3x+y+2
=(x+3y)(x-y)+x+3y+2(x-y)+2
=(x+3y+2)(x-y+1)
3)6x^2-7x-4
=6(x-7/12)^2-49/24-4
=6(x-7/12)^2-145/24
=6[(x-7/12)^2-145/144]
=6[x-(7+√145)/12][x-(7-√145)/12]