Question

几道数学题，因式分解

1　　x^2+x^2y-6y^2-5y-1
2 x^2-2y^2-2z^2-xy+5yz-xz
第一题是x^4+x^2y-6y^2-5y-1

Answer 1

1　　x^2+x^2y-6y^2-5y-1
=x^2(1+y)- 这里的符号写错了吧？
2 x^2-2y^2-2z^2-xy+5yz-xz
=x^2-(y+z)x-(2y^2-5yz+2z^2)
=x^2-（y+z)x-(2y-z)(y-2z)
=(x+2y-z)(x+y-2z)

追问

不好意思啊，是x^4+x^2y-6y^2-5y-1

追答

x^4+x^2y-6y^2-5y-1
=(x^2）^2+yx^2-(6y^2+5y+1)
=(x^2）^2+yx^2-(3y+1)(2y+1)
=(x^2+3y+1)(x^2-2y-1)

Answer 2

解：①原式=(x²+x²y)-(6y²+5y+1)=x²(y+1)-(6y-1)(y+1)-2 (实数范围无法分解)
②原式=x²-(y+z)x-(2y²+2z²-5yz)=x²-(y+z)x-(2y-z)(y-2z)=(x+2y-z)(x-y+2z)