`a)(6x^3-7x^2-x+2):(2x+1)`

`=(6x^3+3x^2-10x^2-5x+4x+2):(2x+1)`

`=[3x^2(2x+1)-5x(2x+1)+2(2x+1)]:(2x+1)`

`=[(3x^2-5x+2)(2x+1)]:(2x+1)`

`=3x^2-5x+2`

`b)(x^4-x^3+x^2+3x):(x^2-2x+3)`

`=(x^4-2x^3+3x^2+x^3-2x^2+3x):(x^2-2x+3)`

`=[x^2(x^2-2x+3)+x(x^2-2x+3)]:(x^2-2x+3)`

`=[(x^2-2x+3)(x^2+x)]:(x^2-2x+3)`

`=x^2+x`

`c)(x^2-y^2+6x+9):(x+y+3)`

`=[(x+3)^2-y^2]:(x+y+3)`

`=[(x-y+3)(x+y+3)]:(x+y+3)`

`=x-y+3`

`d)(x^2+12x-y^2+36):(x-y+6)`

`=[(x+6)^2-y^2]:(x-y+6)`

`=[(x-y+6)(x+y+6)]:(x-y+6)`

`=x+y+6`

`2/3x(x^2-4)=0 `

`<=>x(x-2)(x+2)=0`

`<=>[(x=0),(x=2),(x=-2):}`

`=>S={0;2;-2}`

`b)(x+2)^2-(x-2)(x+2)=0`

`<=>(x+2)(x+2-x+2)=0`

`<=>4(x+2)=0`

`<=>x+2=0`

`<=>x=-2`

`=>S={-2}`

`c)x+2x^2+x^3=0`

`<=>x(x^2+2x+1)=0`

`<=>x(x+1)^2=0`

`<=>x(x+1)=0`

`<=>[(x=0),(x=-1):}`

`=>S={0;-1}.`

Bài `1:`

`a)`

`(6x^3 - 7x^2 - x + 2) : (2x+1)`

`=  [(6x^3 - 10x^2 + 4x) + (3x^2 - 5x +2) ] : (2x+1)`

` = [ 2x (3x^2 - 5x + 2) + (3x^2 - 5x + 2)] : (2x+1)`

`=  (2x+1)(3x^2 - 5x + 2) : (2x+1)`

`=  3x^2 - 5x + 2`

`b)`

`(x^4 - x^3 + x^2 + 3x) : (x^2 - 2x + 3)`

`=  [ (x^4 - 2x^3 + 3x^2) + (x^3 - 2x^2 + 3x)] : (x^2 - 2x+3)`

`=  [ x^2 (x^2 - 2x + 3) + x (x^2 - 2x + 3) ] : (x^2 - 2x+3)`

` = (x^2 + x)(x^2 - 2x + 3) : (x^2 - 2x+3)`

` = x^2+  x`

`c)`

`(x^2 - y^2 + 6x + 9) : (x + y+ 3)`

`=  [ (x^2 + 6x + 9) - y^2] : (x+y+3)`

`=  [ (x+3)^2-  y^2] : (x+y+3)`

` = (x + 3 - y)(x+3+y) : (x+y+3)`

` = x + 3 - y`

`d)`

`(x^2 + 12x - y^2 + 36)  : (x-y +6)`

` = [ (x^2 + 12x + 36) - y^2] : (x-y + 6)`

` = [ (x+6)^2 - y^2] : (x-y+6)`

`=  (x + 6 - y)(x + 6+  y) : (x-y + 6)`

`=  x+6+y`

Bài `2:`

`a)`

`2/3x (x^2 -4) =0`

`=> x=  0` hoặc `x^2 - 4=0`

`+) x = 0`

`+) x^2 - 4 = 0`

`=> x^2 = 4`

`=> x^2 = (+-2)^2`

`=> x = +-2`

Vậy `x \in {0 ; 2 ; -2}`

`b)`

`(x+2)^2 - (x-2)(x+2) =0`

`=> (x+2) [ (x+2) - (x-2)] = 0`

`=> (x+2) . (x + 2 - x + 2) = 0`

`=> (x+2) . 4 =0`

`=>x+2=0`

`=>x=-2`

Vậy `x=-2`

`c)`

`x + 2x^2+  x^3 = 0`

`=> x (1 + 2x + x^2) = 0`

`=> x (x + 1)^2=  0`

`=> x=0` hoặc `(x+1)^2=0`

`+) x=0`

`+) (x+1)^2= 0`

`=> x +  1=0`

`=>x=-1`

Vậy `x \in {0;-1}`