Question

因式分解练习题

6x^2-7xy-3y^2-xz+7yz-2z^2
2x^4-x^3-6x^2-x+2
(x+1)^4+(x+3)^4-272
xy(xy+1)+(xy+3)-2(x+y+0.85)-(x+y-1)^2
x^3+8y^3-z^3+6xyz
x^2+5xy+6y^2+8x+18y+12
x^2+2xy-8y^2+2x+14y-3

Answer 1

1.6X^2-7xy-3y^2-xz+7yz-2z^2=(3x+y-2z)(2x-3y+z)

2.（2x-1）(x^3-3x-2)=(2x-1)[x(x-2)(x+2)+(x-2)]
=（2x-1）(x-2)(x^2+2x+1)=（2x-1）(x-2)(x+1)^2

3.（x+1）^4+(x+3)^4-272
=(x+3)^4-4^4+(x+1)^4-2^4
（平方差）
=[(x+3)^2-4^2][(x+3)^2+4^2]+[(x+1)^2-2^2][(x+1)^2+2^2]
（平方差）
=(x-1)(x+7)[(x+3)^2+4^2]+(x-1)(x+3)[(x+1)^2+2^2]
（提取公因式，再整理）
=2(x-1)（x^2+4x+19)(5+x)

4. xy(xy+1)+(xy+3)-2(x+y+0.85)-(x+y-1)^2=(xy)^2-x^2-y^2+0.3

5.x^3+8y^3-z^3+6xyz=(x+2y-z)(x^2+4y^2+z^2-2xy+xz-2yz)

6.原式=(x+2y+2)(x+3y+6)．

7.x^2+2xy-8y^2+2x+14y-3
=(x^2+2xy-8y^2)-(x-2y)+3(x+4y)-3
=(x-2y)(x+4y)-(x-2y)+3(x+4y)-3
=(x-2y+3)(x+4y-1).

Answer 2

2、x^2（x-2）(2x+3-1)