Question

phân tích đa thức thành nhân tử

x³-7x-6

làm bằng nhiều cách

Answer 1

Cách 1:

\(x^3-7x-6=x^3+x^2-x^2-x-6x-6\)

\(=\left(x^3+x^2\right)-\left(x^2+x\right)-\left(6x+6\right)\)

\(=x^2.\left(x+1\right)-x.\left(x+1\right)-6.\left(x+1\right)\)

\(=\left(x+1\right).\left(x^2-x-6\right)\)

\(=\left(x+1\right).\left(x^2+2x-3x-6\right)\)

\(=\left(x+1\right).\left[\left(x^2+2x\right)-\left(3x+6\right)\right]\)

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

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

Chúc bạn học tốt!!!

Answer 2

Cách 2:

\(x^3-7x-6=x^3-3x^2+3x^2-9x+2x-6\)

\(=\left(x^3-3x^2\right)+\left(3x^2-9x\right)+\left(2x-6\right)\)

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

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

\(=\left(x-3\right).\left[\left(x^2+x\right)+\left(2x+2\right)\right]\)

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

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

Chúc bạn học tốt!!!

Answer 3

\(x^3-7x-6\)

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

= \(x^2\left(x+1\right)-x\left(x+1\right)-6\left(x+1\right)\)

= \(\left(x+1\right)\left(x^2-x-6\right)\)

= \(\left(x+1\right)\left(x^2-3x+4x-6\right)\)

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

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

Answer 4

Cách 3:

\(x^3-7x-6=x^3+2x^2-2x^2-4x-3x-6\)

\(=\left(x^3+2x^2\right)-\left(2x^2+4x\right)-\left(3x+6\right)\)

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

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

\(=\left(x+2\right).\left[\left(x^2+x\right)-\left(3x+3\right)\right]\)

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

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

Chúc bạn học tốt!!!

Answer 5

CÁCH 4 :

\(x^3-7x-6\)

\(=x^3-27-7x+21\)

\(=\left(x-3\right)\left(x^2+3x+9\right)-7\left(x-3\right)\)

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

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

Answer 6

CÁCH 5 :

\(x^3-7x-6\)

\(=7x^3-6x^3-7x-6\)

\(=\left(7x^3-7x\right)-\left(6x^3+6\right)\)

\(=7x\left(x^2-1\right)-6\left(x^3+1\right)\)

\(=7x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\left(x^2-x+1\right)\)

\(=\left(x+1\right)\left[7x\left(x-1\right)-6x^2+6x-6\right]\)

\(=\left(x+1\right)\left(7x^2-7x-6x^2+6x-6\right)\)

\(=\left(x+1\right)\left(x^2-x-6\right)\)

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

Answer 7

CÁCH 6 :

\(x^3-7x-6\)

\(=x^3+1-7x-7\)

\(=\left(x+1\right)\left(x^2-x+1\right)-7\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-x-6\right)\)

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

Answer 8

CÁCH 7 :

\(x^3-7x-6\)

\(=x^3-4x-3x-6\)

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

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

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

Answer 9

x^3-7x-6=x^3-x-6x-6=x(x^2-1^2)-6(x-1)

=x(x-1)(x+1)-6(x-1)=(x-1)[x(x+1)-6]=

(x-1)(x^2+x-6)