x^2就表示平方,依次,x^3表示3次方
1.12x^2-6x-2x+1+3x^2-3x-x+1+x^2=16x^2-12x+2=(2x^2-1)(8x^2-2)=2(x^2-1)(2x^2-1)
2.令x^3=t,
则原式=t^3+t^2+t-3,令t^3+t^2+t-3,发现t=1是方程的根,(t^3+t^2+t-3)/(t-1)=t^2+2t+3,
所以t^3+t^2+t-3=(t-1)(t^2+2^t+3)
x九次方+x六次方+x三次方-3=(x^3-1)(x^6+2x^3+3)=(x-1)(x^2+x+1)(x^6+2x^3+3)
3.6x^4+7x^3-36x^2-7x+6
=(6x^4+x^3-x^2)+(6x^3+x^2-x)+(-36x^2-6x+6)
=x^2(6x^2+x-1)+x(6x^2+x-1)-6(6x^2+x-1)
=(6x^2+x-1)(x^2+x-6)
=(2x+1)(3x-1)(x-2)(x+3).
4.a^3b-ab^3+a^2+b^2+1
=a^3b-a^2b^2+a^2b^2+ab-ab-ab^3+a^2+b^2+1
=a^3b-a^2b^2+ab+a^2b^2-ab^3+b^2+a^2-ab+1
=ab(a^2-ab+1)+b^2(a^2-ab+1)+1(a^2-ab+1)
=(ab+b^2+1)(a^2-ab-1)
5,3x^2-11xy+6y^2-xz-4yz-2z^2
=(3x^2-11xy+6y^2)+(2xz-6yz)-(3xz+2yz)-2z^2
=(3x-2y)(x-3y)+2z(x-3y)-z(3x-2y)-2z^2
=(x-3y)(3x-2y+2z)-z(3x-2y+2z)
=(3x-2y+2z)(x-3y-z)
6.x^2-8xy+15y^2+2x-4y-3
＝x^2-8xy+16y^2- y^2+2x-4y-3
＝(x-4y)^2- y^2+2y-1-(2y-1)+2x-4y-3
＝(x-4y)^2-(y-1)^2+2x-6y-2
＝(x-4y-(y-1)) (x-4y+(y-1))+2(x-3y-1)
＝(x-5y+1) (x-3y-1)+2(x-3y-1)
＝(x-5y+1+2) (x-3y-1)
＝(x-5y+3) (x-3y-1)