Question

Phân tích các đa thức sau thành nhân tử

1) x^3+2x-3

2) x^3-6x+4

3) x^3-2x^2+1

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

5) x^3-6x+9x

6) 4x^3-9x^2+5x

Answer 1

1) \(x^3+2x-3\)

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

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

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

2) \(x^3-6x+4\)

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

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

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

Answer 2

3) \(x^3-2x^2+1\)

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

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

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

4) \(x^3+5x^2-12\)

\(=\left(x^3+2x^2\right)+\left(3x^2+6x\right)-\left(6x+12\right)\)

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

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

Answer 3

5) \(x^3-6x^2+9x\) (chắc đề như vậy)

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

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

6) \(4x^3-9x^2+5x\)

\(=x\left(4x^2-9x+5\right)\)

\(=x\left[\left(4x^2-4x\right)-\left(5x-5\right)\right]\)

\(=x\left[4x\left(x-1\right)-5\left(x-1\right)\right]\)

\(=x\left(x-1\right)\left(4x-5\right)\)

Answer 4

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

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

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

\(x^3+5x^2-12=\left(x+2\right)\left(x^3+3x-6\right)\)

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

\(4x^3-9x^2+5x=x\left(x-1\right)\left(4x-5\right)\)