Question

Phân tích đa thức thành nhân tử

a, x (a-b)+a-b

b,-a-b+x(a+b)

c,xz+yz-5(x+y)

d,x^2-6x+9

e,4x^2-3x-1

F,(x^2-2x)^2-3x^2+6x-4

Answer 1

`x(a-b) + (a-b) = (x+1)(a-b) `

`-a-b + x(a+b) = -(a+b) + x(a+b) = (x-1)(a+b) `

`xz + yz - 5 (x + y) = z(x+y) + 5(x+y) = (z+5)(x+y)`

`x^2 - 6x + 9 = x^2 - 3x - 3x + 9 = (x^2 - 3x) - (3x - 9) = (x - 3)(x-3) `

`4x^2 - 3x - 1 = 4x^2 - 4x + x - 1 = (4x^2 - 4x) + (x-1) = (4x + 1)(x-1) `

`(x^2 - 2x)^2 - 3x^2 + 6x - 4`

`= (x^2 - 2x)^2 - 3(x^2 - 2x) - 4`

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

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

`= (x^2 -2x - 4)(x^2 - 2x + 1)`

`= (x^2 -2x - 4)(x^2 - x - x + 1)`

`= (x^2 -2x - 4)[(x^2 - x) - (x - 1)]`

`= (x^2 -2x - 4)(x-1)(x - 1) `