Phân tích đa thức sau thành nhân tử x³ – 7x – 6 (bằng nhiều cách)

Lời giải

Lời giải

Cách 1.

x³ – 7x – 6

= x³ – x – 6x – 6

= x(x² – 1) – 6(x + 1)

= x(x + 1)(x – 1) – 6(x + 1)

= (x – 1) [x(x + 1) – 6]

= (x – 1)(x² + x – 6)

Cách 2.  

x³ – 7x – 6

= x³ – x² + x² – x – 6x  – 6

= x²(x – 1) + x(x – 1) – 6(x – 1)

= (x – 1)(x² + x – 6)

Cách 3.

x³ – 7x – 6

= 7x³ – 7x – 6x³ – 6

= 7x(x² – 1) – 6(x³ – 1)

= 7x(x – 1)(x + 1) – 6(x – 1)(x² + x + 1)

 = (x – 1)[7x(x + 1) – 6(x² + x + 1)]

= (x – 1)(7x² + 7x – 6x² – 6x – 6)

= (x – 1)(x² + x – 6)

Cách 5.

x³ – 7x – 6

= x³ – 4x – 3x – 6

= x(x² – 4) – 3(x + 2)

= x(x + 2)(x – 2) – 3(x + 2)

= (x + 2)[x(x – 2) – 3]

= (x + 2)(x² – 2x – 3)

Cách 6.

x³ – 7x – 6

= x³ – 9x + 2x – 6

= x(x² – 9) + 2(x – 3)

= x(x + 3)(x – 3) + 2(x – 3)

= (x – 3)[x(x + 3) + 2]

= (x – 3)(x² + 3x + 2)