Question

因式分解3x^2+5xy-2y^2+x+9y-4

Answer 1

3x²+5xy-2y²+x+9y-4

用待定系数法做

因为3x²+5xy-2y²=(3x-y)(x+2y)

所以设3x²+5xy-2y²+x+9y-4=(3x-y+a)(x+2y+b)
=3x²+5xy-2y²+ax+2ay+3bx-by+ab
=3x²+5xy-2y²+(a+3b)x+(2a-b)y+ab

比较系数，得 a+3b=1, 2a-b=9, ab=-4

解得 a=4，b=-1

所以3x²+5xy-2y²+x+9y-4=(3x-y+4)(x+2y-1)

Answer 2

3X^2+5XY-2Y^2+X+9Y-4
=(x+2y)(3x-y)+x+9y-4
=(x+2y)(3x-y)+(4x+8y-3x+y)-4
=(x+2y)(3x-y)+4(x+2y)-(3x-y)-4
=(x+2y)(3x-y) -(3x-y)+4(x+2y) -4
=(x+2y-1)(3x-y)+4(x+2y-1)
=(x+2y-1)(3x-y+4)

Answer 3

3x^2+5xy-2y^2+x+9y-4=(x+2y-1)(3x-y+4)