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!!!

phân tích đa thức thành nhân tử

a2(b-c)+b2(c-a)+c2(a-b)

Ta có: \(a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)\)

= \(a^2\left(b-c\right)+b^2\left[\left(c-b\right)+\left(b-a\right)\right]+c^2\left(a-b\right)\)

= \(a^2\left(b-c\right)-b^2\left(b-c\right)-b^2\left(a-b\right)+c^2\left(a-b\right)\)

= \(\left(b-c\right)\left(a^2-b^2\right)-\left(a-b\right)\left(b^2-c^2\right)\)

= \(\left(b-c\right)\left(a-b\right)\left(a+b\right)-\left(a-b\right)\left(b-c\right)\left(b+c\right)\)

= \(\left(a-b\right)\left(b-c\right)\left(a+b-b-c\right)\)

= \(\left(a-b\right)\left(b-c\right)\left(a-c\right)\)