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 !
\(8-12x+6x^2-x^3\)
\(=\left(2-x\right)^3\)
\(125x^3-75x^2+15x-1\)
\(=\left(5x-1\right)^3\)
\(x^2-xz-9y^2+3yz\)
\(=\left(x-3y\right)\left(x+3y\right)-z\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y-z\right)\)
\(x^3-x^2-5x+125\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
\(x^3+2x^2-6x-27\)
\(=x^3+5x^2+9x-3x^2-15x-27\)
\(=x\left(x^2+5x+9\right)-3\left(x^2+5x+9\right)\)
\(=\left(x-3\right)\left(x^2+5x+9\right)\)
\(12x^3+4x^2-27x-9\)
\(=4x^2\left(3x+1\right)-9\left(3x+1\right)\)
\(=\left(3x+1\right)\left(4x^2-9\right)\)
\(=\left(3x+1\right)\left(2x-3\right)\left(2x+3\right)\)
\(4x^4+4x^3-x^2-x\)
\(=4x^3\left(x+1\right)-x\left(x+1\right)\)
\(=x\left(x+1\right)\left(4x^2-1\right)\)
\(=x\left(x+1\right)\left(2x-1\right)\left(2x+1\right)\)
