Question

[Bùi Thành Long]

Bài 1: Phân tích đa thức thành nhân tử:

1) 8 - 12x + 6x2 - x3

2) 125x3 - 75x2 +15x -1

3) x2 - xz - 9y2 + 3xyz

4) x3 -x -5x +125

5) x3 + 2x2 - 6x - 27

6) 12x3 + 4x2 -27x - 9

7) 4x4 + 4x3 - x2 - x

8) x6 - x4 - 9x3 + 9x2

9) x4 - 4x3 + 8x2 -16x + 16

10) 3a2 - 6ab + 3b2 -12c2

11) a2 + 2ab + b2 - ac - bc

12) ac - bc - a2 + 2ab - b2

13) (x - y + 5)2 - 2(x - y + 5) + 1

14) x8 + x7 + 1

15) x8 + x4 +1

16) x5 + x + 1

17) x3 + x2 + 4

18) x4 + 2x2 - 24

19) x3 - 2x - 4

20) x2 + 4x + 3

LÀM CHI TIẾT HỘ MÌNH NHÉ !

  

Answer 1

[Phương An]

\(8-12x+6x^2-x^3\)

\(=\left(2-x\right)^3\)

\(125x^3-75x^2+15x-1\)

\(=\left(5x-1\right)^3\)

\(x^2-xz-9y^2+3yz\)

\(=\left(x-3y\right)\left(x+3y\right)-z\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x+3y-z\right)\)

\(x^3-x^2-5x+125\)

\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)

\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)

\(=\left(x+5\right)\left(x^2-6x+25\right)\)

\(x^3+2x^2-6x-27\)

\(=x^3+5x^2+9x-3x^2-15x-27\)

\(=x\left(x^2+5x+9\right)-3\left(x^2+5x+9\right)\)

\(=\left(x-3\right)\left(x^2+5x+9\right)\)

\(12x^3+4x^2-27x-9\)

\(=4x^2\left(3x+1\right)-9\left(3x+1\right)\)

\(=\left(3x+1\right)\left(4x^2-9\right)\)

\(=\left(3x+1\right)\left(2x-3\right)\left(2x+3\right)\)

\(4x^4+4x^3-x^2-x\)

\(=4x^3\left(x+1\right)-x\left(x+1\right)\)

\(=x\left(x+1\right)\left(4x^2-1\right)\)

\(=x\left(x+1\right)\left(2x-1\right)\left(2x+1\right)\)