Question

分解因式：3x²+5xy－2y²﹢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

原式=(3x-y)(x+2y)+x+9y-4
十字相乘
3x-y 4
×
x+2y -1
x系数-3+4=1
y系数1+8=9
符合
所以原式=(3x-y+4)(x+2y-1)

追问

为什么可以十字相乘啊

追答

就是可以啊

Answer 3

3x²+5xy－2y²﹢x﹢9y－4
=(3x-y)(x+2y)+x+9y-4
=(3x-y)(x+2y)+4x+8y-3x+y-4
=(3x-y)(x+2y)+4(x+2y)-(3x-y)-4
=(3x-y+4)(x+2y-1)

Answer 4

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