x^2-8xy+15y^2+2x-4y-3=(x-3y-1)(x-5y+3)
x^2-xy+2x+y-3
=(x^2+2x-3)-xy+y
=(x+3)(x-1)-y(x-1)
=(x-1)(x-y+3)
3x^2-11xy+6y^2-xz-4yz-2z^2
=3x^2-11xy+6y^2-(3xz-2xz)-(6yz+2yz)-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)
x^3+x^2-10x-6
=x^3+(4x^2-3x^2)-(12x-2x)-6
=(x^3-3x^2)-(4x^2-12x)+(2x-6)
=(x-3)(x^2-4x+2)
x^4+3x^3-3x^2-12x-4
=x^4+3x^3-(5x^2-2x^2)-12x-4
=(x^4+3x^3+2x^2)-(5x^2+12x+4)
=x^2(x^2+3x+2)-(5x+2)(x+2)
=x^2(x+2)(x+1)-(5x+2)(x+2)
=(x+2)[x^2(x+1)-(5x+2)]
=(x+2)(x^3+x^2-5x+2)
4x^4+4x^3-9x^2-x+2
=4x^4+4x^3-(8x^2+x^2)-x+2
=(4x^4+4x^3-8x^2)-(x^2+x-2)
=4x^2(x^2+x-2)-(x^2+x-2)
=(4x^2-1)(x^2+x-2)
=(2x-1)(2x+1)(x-2)(x+1)
2x^2+3xy-9y^2+14x-3y+20=(x+3y+5)(2x-3y+4)
x^4+5x^3+15x-9
=(x^4-9)+(5x^3+15x)
=(x^2+3)(x^2-3)+5x(x^2+3)
=(x^2+3)(x^2-3+5x)
