Question

两道七年级因式分解

(1) x^2 + xy - 6y^2 - x + 7y - 2
(2) 6x^2 + xy - 2y^2 + 2x - 8y - 8

Answer 1

待定系数法
设x^2+xy-6y^2-x+7y-2=(ax+by+c)*(dx+ey+f)
=ad*x^2+(ae+bd)*xy+be*y^2+(af+cd)*x+(bf+ce)*y+cf
ad=1
ae+bd=1
be=-6
af+cd=-1
bf+ce=7
cf=-2
令a=1,可以得到
a=1,b=3,c=-2,d=1,e=-2,f=1
x^2+xy-6y^2-x+7y-2=(x+3y-2)*(x-2y+1)

同理
6x^2+xy-2y^2+2x-8y-8=(2x-y-2)*(3x+2y+4)

Answer 2

(1) x^2 + xy - 6y^2 - x + 7y - 2

=(x+3y)(x-2y)+[(x+3y)*(+1)+(x-2y)*(-2)]-2
=(x+3y-2)(x-2y+1)

(2) 6x^2 + xy - 2y^2 + 2x - 8y - 8

=(2x-y)(3x+2y)+[(2x-y)*4+(3x+2y)(-2)]-8

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

Answer 3

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