6x^2+7xy+2y^2-8x-5y+2 因式分解
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/30 06:48:55
6x^2+7xy+2y^2-8x-5y+2 因式分解
如题
如题
![6x^2+7xy+2y^2-8x-5y+2 因式分解](/uploads/image/z/18822450-66-0.jpg?t=6x%5E2%2B7xy%2B2y%5E2-8x-5y%2B2+%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3)
6x^2+7xy+2y^2-8x-5y+2
=(2x+y)(3x+2y)-8x-5y+2
下面我们用待定系数法来解答
(2x+y)(3x+2y)-8x-5y+2=(2x+y+m)(3x+2y+n)
=6x^2+7xy+2y^2+(3m+2n)x+(n+2m)y+mn
mn=2
3m+2n=-8
n+2m=-5
n=-1
m=-2
(2x+y)(3x+2y)-8x-5y+2=(2x+y-2)(3x+2y-1)
=(2x+y)(3x+2y)-8x-5y+2
下面我们用待定系数法来解答
(2x+y)(3x+2y)-8x-5y+2=(2x+y+m)(3x+2y+n)
=6x^2+7xy+2y^2+(3m+2n)x+(n+2m)y+mn
mn=2
3m+2n=-8
n+2m=-5
n=-1
m=-2
(2x+y)(3x+2y)-8x-5y+2=(2x+y-2)(3x+2y-1)