Bài 2:
Cách 1:
\(x^3-7x-6=x^3-3x^2+3x^2-9x+2x-6\)
\(=\left(x^3-3x^2\right)+\left(3x^2-9x\right)+\left(2x-6\right)\)
\(=x^2.\left(x-3\right)+3x.\left(x-3\right)+2.\left(x-3\right)\)
\(=\left(x-3\right).\left(x^2+3x+2\right)\)
\(=\left(x-3\right).\left(x^2+x+2x+2\right)\)
\(=\left(x-3\right).\left[\left(x^2+x\right)+\left(2x+2\right)\right]\)
\(=\left(x-3\right).\left[x.\left(x+1\right)+2.\left(x+1\right)\right]\)
\(=\left(x-3\right).\left(x+1\right).\left(x+2\right)\)
Cách 2:
\(x^3-7x-6=x^3+x^2-x^2-x-6x-6\)
\(=\left(x^3+x^2\right)-\left(x^2+x\right)-\left(6x+6\right)\)
\(=x^2.\left(x+1\right)-x.\left(x+1\right)-6.\left(x+1\right)\)
\(=\left(x+1\right).\left(x^2-x-6\right)\)
\(=\left(x+1\right).\left(x^2+2x-3x-6\right)\)
\(=\left(x+1\right).\left[\left(x^2+2x\right)-\left(3x+6\right)\right]\)
\(=\left(x+1\right).\left[x.\left(x+2\right)-3.\left(x+2\right)\right]\)
\(=\left(x+1\right).\left(x+2\right).\left(x-3\right)\)
Chúc bạn học tốt!!! Còn 1 cách nữa nhưng mình mỏi tay quá!!! 
a, \(x^3-9x^2+6x+16=x^3+x^2-10x^2-10x+16x+16\)
\(=\left(x^3+x^2\right)-\left(10x^2+10x\right)+\left(16x+16\right)\)
\(=x^2.\left(x+1\right)-10x.\left(x+1\right)+16.\left(x+1\right)\)
\(=\left(x+1\right).\left(x^2-10x+16\right)\)
\(=\left(x+1\right).\left(x^2-2x-8x+16\right)\)
\(=\left(x+1\right).\left[\left(x^2-2x\right)-\left(8x-16\right)\right]\)
\(=\left(x+1\right).\left[x.\left(x-2\right)-8.\left(x-2\right)\right]\)
\(=\left(x+1\right).\left(x-2\right).\left(x-8\right)\)
Chúc bạn học tốt!!!
b, \(x^3-x^2-x-2=x^3-2x^2+x^2-2x+x-2\)
\(=\left(x^3-2x^2\right)+\left(x^2-2x\right)+\left(x-2\right)\)
\(=x^2.\left(x-2\right)+x.\left(x-2\right)+\left(x-2\right)\)
\(=\left(x-2\right).\left(x^2+x+1\right)\)
Chúc bạn học tốt!!!
c, \(x^3+x^2-x+2=x^3+2x^2-x^2-2x+x+2\)
\(=\left(x^3+2x^2\right)-\left(x^2+2x\right)+\left(x+2\right)\)
\(=x^2.\left(x+2\right)-x.\left(x+2\right)+\left(x+2\right)\)
\(=\left(x+2\right).\left(x^2-x+1\right)\)
Chúc bạn học tốt!!!
d, \(x^3-6x^2-x+30=x^3+2x^2-8x^2-16x+15x+30\)
\(=\left(x^3+2x^2\right)-\left(8x^2+16x\right)+\left(15x+30\right)\)
\(=x^2.\left(x+2\right)+8x.\left(x+2\right)+15.\left(x+2\right)\)
\(=\left(x+2\right).\left(x^2+8x+15\right)\)
\(=\left(x+2\right).\left(x^2+3x+5x+15\right)\)
\(=\left(x+2\right).\left[\left(x^2+3x\right)+\left(5x+15\right)\right]\)
\(=\left(x+2\right).\left[x.\left(x+3\right)+5.\left(x+3.\right)\right]\)
\(=\left(x+2\right).\left(x+3\right).\left(x+5\right)\)
Chúc bạn học tốt!!!
Bài 1:
a, \(x^3-9x^2+6x+16\)
\(=x^3-8x^2-x^2+8x-2x+16\)
\(=x^2\left(x-8\right)-x\left(x-8\right)-2\left(x-8\right)\)
\(=\left(x^2-x-2\right)\left(x-8\right)\)
b, \(x^3-x^2-x-2\)
\(=x^3-2x^2+x^2-2x+x-2\)
\(=x^2\left(x-2\right)+x\left(x-2\right)+\left(x-2\right)\)
\(=\left(x^2+x+x\right)\left(x-2\right)\)
c, \(x^3+x^2-x+2\)
\(=x^3+2x^2-x^2-2x+x+2\)
\(=x^2\left(x+2\right)-x\left(x+2\right)+\left(x+2\right)\)
\(\left(x^2-x+1\right)\left(x+2\right)\)
d, \(x^3-6x^2-x+30\)
\(=x^3-5x^2-x^2+5x-6x+30\)
\(=x^2\left(x-5\right)-x\left(x-5\right)-6\left(x-5\right)\)
\(=\left(x^2-x-6\right)\left(x-5\right)\)
Bài 2:
\(x^3-7x-6\)
\(=x^3+6x^2-6x^2-6x-x-6\)
\(=x^2\left(x+6\right)-6x\left(x+6\right)-\left(x+6\right)\)
\(=\left(x^2-6x-1\right)\left(x+6\right)\)
