3x^2+5xy-2y^2+x+9y-4
=(x+2y)(3x-y)+x+9y-4
=(x+2y)(3x-y)+4(x+2y)-(3x-y)-4
=(x+2y-1)(3x-y+4)
x^2+x-(a^2-a)
=(x^2-a^2)+x+a
=(x+a)(x-a)+(x+a)
=(x+a)(x-a+1)
3x^2+4xy-y^2
= 3(x^2+ xy*4/3 - y^2*1/3)
= 3[(x^2+ 2*2/3 *xy +4/9y^2) - y^2/3- 4/9y^2]
= 3[(x+2/3y)^2 - 7/9 y^2]
=3(x+2/3y +√7/3y)(x+2/3y - √7/3y)
= 3[x+(2+√7)/3y][x+(2-√7)/3y]