因式分解狂人进!1.2x^2+xy-y^2-4x+5y-62.(x-3)(x-1)(x+2)(x+4)-1443.(x^2+xy+y^2)^2-4xy(x^2+y^2)4.2x^4-11x^3+22x^2-19x+65.xyz-2xy-2yz-2xz+4x+4y+4z-86.2x^3+11x^2+17x+6狂人们,看你们的了!

Question

因式分解狂人进!
1.2x^2 + xy - y^2 - 4x + 5y - 6
2.(x-3)(x-1)(x+2)(x+4)-144
3.(x^2 + xy + y^2)^2 - 4xy(x^2 + y^2)
4.2x^4 - 11x^3 + 22x^2 - 19x + 6
5.xyz-2xy-2yz-2xz+4x+4y+4z-8
6.2x^3 + 11x^2 + 17x + 6
狂人们,看你们的了!

Answer 1

1.2x^2 + xy - y^2 - 4x + 5y - 6
=(2x-y)(x+y)-(6x-3y)+2x+2y-6
=(2x-y)(x+y)-3(2x-y)+2x+2y-6
=(x+y-3)(2x-y)+2(x+y-3)
=(x+y-3)(2x-y+2)
2.(x-3)(x-1)(x+2)(x+4)-144
=[(x-3)(x+4)][(x-1)(x+2)]-144
=[(x^2+x)-12][(x^2+x)-2]-144
=(x^2+x)^2-14(x^2+x)+24-144
=(x^2+x)^2-14(x^2+x)-120
=(x^2+x-20)(x^2+x+6)
=(x-4)(x+5)(x^2+x+6)
3.(x^2 + xy + y^2)^2 - 4xy(x^2 + y^2)
=[(x^2+y^2)+xy]^2-4xy(x^2+y^2)
=(x^2+y^2)^2+2xy(x^2+y^2)+x^2y^2-4xy(x^2+y^2)
=(x^2+y^2)^2-2xy(x^2+y^2)+x^2y^2
=(x^2+y^2-xy)^2
4.2x^4 - 11x^3 + 22x^2 - 19x + 6
=(2x^4-2)-(11x^3-11)+22x^2-19x-3
=2(x^2+1)(x+1)(x-1)-11(x-1)(x^2+x+1)+(22x+3)(x-1)
=(x-1)(2x^3+2x^2+2x+2-11x^2-11x-11+22x+3)
=(x-1)(2x^3-9x^2+13x-6)
=(x-1)[(2x^3-2)-(9x^2-13x+4)]
=(x-1)[2(x-1)(x^2+x+1)-(9x-4)(x-1)]
=(x-1)^2(2x^2+2x+2-9x+4)
=(x-1)^2(2x^2-7x+6)
=(x-1)^2(x-2)(2x-3)
5.xyz-2xy-2yz-2xz+4x+4y+4z-8
=(xyz-2xy)-(2yz-4y)-(2xz-4x)+(4z-8)
=xy(z-2)-2y(z-2)-2x(z-2)+4(z-2)
=(z-2)(xy-2y-2x+4)
=(z-2)[(xy-2y)-(2x-4)]
=(z-2)[y(x-2)-2(x-2)]
=(z-2)(y-2)(x-2)
6.2x^3 + 11x^2 + 17x + 6
=(2x^3+16)+(11x^2+17x-10)
=2(x+2)(x^2-2x+4)+(11x-5)(x+2)
=(x+2)(2x^2-4x+8+11x-5)
=(x+2)(2x^2+7x+3)
=(x+2)(2x+1)(x+3)