1.2x^2+3xy-9y^2+14x-3y+20

1.2x^2+3xy-9y^2+14x-3y+20
=(2x-3y)(x+3y)+(10x-15y)+4x+12y+20
=(2x-3y)(x+3y+5)+4(x+3y+5)
=(2x-3y+4)(x+3y+5)
2.6x^4+7x^3-36x^2-7x+6
=(6x^4-24x^2)+(7x^3-14x^2)+2x^2-7x+6
=6x^2(x+2)(x-2)+7x^2(x-2)+(2x-3)(x-2)
=(x-2)(6x^3+19x^2+2x-3)
=(x-2)[(6x^3+18x^2)+(x^2+2x-3)]
=(x-2)[6x^2(x+3)+(x-1)(x+3)]
=(x-2)(x+3)(6x^2+x-1)
=(x-2)(x+3)(3x-1)(2x+1)
3.(x^2+xy+y^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
=(x^2-xy+y^2)^2
4.(m^2-1)(n^2-1)+4mn
=m^2n^2-m^2-n^2+1+4mn
=(m^2n^2+2mn+1)-(m^2-2mn+n^2)
=(mn+1)^2-(m-n)^2
=(mn+m-n+1)(mn-m+n+1)
5.(x^2+3x+2)(4x^2+8x+3)-90
=(x+1)(x+2)(2x+1)(2x+3)-90
=[(x+1)(2x+3)][x+2)(2x+1)]-90
=[(2x^2+5x)+3][(2x^2+5x)+2]-90
=(2x^2+5x)^2+5(2x^2+5x)+6-90
=(2x^2+5x)^2+5(2x^2+5x)-84
=(2x^2+5x-7)(2x^2+5x+12)
=(2x+7)(x-1)(2x^2+5x+12)

1. 2x^2+3xy-9y^2+14x-3y+20
=(2x-3y)(x+3y)+(14x-3y)+20
=(2x-3y+4)(x+3y+5)
2. 6x^4+7x^3-36x^2-7x+6
=(6x^4-12x^3)+(19x^3-38x^2)+(2x^2-4x)-(3x-6)
=(6x^3+19x^2+2x-3)(x-2)
=[(6x^3+18...

2x^2+3xy-9y^2+14x-3y+20=(2x-3y+4)(x+3y+5)