Question

Phân tích đa thức thành nhân tử bằng phương pháp đặt ẩn phụ

x⁴+2x³+5x²+4x-12

Answer 1

hi

Answer 2

`x^4+2x^3+5x^2+4x-12`

`=x^4-x^3+3x^3-3x^2+8x^2-8x+12x-12`

`=x^3(x-1)+3x^2(x-1)+8x(x-1)+12(x-1)`

`=(x-1)(x^3+3x^2+8x+12)`

`=(x-1)(x^3+2x^2+2x^2+4x+6x+12)`

`=(x-1)[x^2(x+2)+2x(x+2)+6(x+2)]`

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

Answer 3

\(x^4+2x^3+5x^2+4x-12\)

\(=x^4-x^3+3x^3-3x^2+8x^2-8x+12x-12\)

\(=\left(x-1\right)\left(x^3+3x^2+8x+12\right)\)

\(=\left(x-1\right)\left(x^2+2x^2+x^2+2x+6x+12\right)\)

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