因式分解方面的题目

1。以知多项式x^3+px-2能被x^2+mx-1整除，求p,m.
设(x^2+mx-1)(x+a)=x^3+px-2
(x^2+mx-1)(x+a)=x^3+ax^2+mx^2+amx-x-a=x^3+(a+m)x^2+(am-1)x-a
上下对照可知
a=2
a+m=0
m=-2
p=am-1
p=-5
所以p=-5,m=-2
2.(x+y)(x-y)-4(y-1)
此题有问题
是(x+y)(x-y)-4(y+1)
=x^2-y^2-4y-4
=x^2-(y^2+4y+4)
=x^2-(y+2)^2
=(x+y+2)(x-y-2)

3.(x+y)^3+2xy(1-x-y)-1
=(x+y)^3-1+2xy(1-x-y)
=(x+y-1)(x^2+2xy+y^2+x+y+1)-2xy(x+y-1)
=(x+y-1)(x^2+y^2+x+y+1)

1。x^3+px-2=（x^2+mx-1）(x+2)
=x^3+(2+m)x^2+(2m-1)x-2
2+m=0---->m=-2
p=2m-1=-5

2.(x+y)(x-y)-4(y+1)
=x^2-y^2-4y-4
=x^2-(y-2)^2
=(x+y-2)(x-y+2)

3.(x+y)^3+2xy(1-x-y)-1
=(x+y-1)[(x+y)^2+(x+y)+1]-2xy(x+y-1)
=(x+y-1)(x^2+y^2+x+y+1)