Question

[Kristein Gin]

phân tích đa thức thành nhân tử.

1. 3x² + 2x – 1
2. x³ + 6x² + 11x + 6
3. x⁴ + 2x² – 3
4. ab + ac +b² + 2bc + c²
5. a³ – b³ + c³ + 3abc

Answer 1

[Hà Thị Quỳnh]

Ta có 

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

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

2, \(x^3+2x^2+4x^2+8x+3x+6\)

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

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

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

\(=\left(x+2\right)\text{[}x\left(x+1\right)+3\left(x+1\right)\text{]}\)

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

3,\(x^4+2x^2-3=x^4-x^2+3x^2-3\)

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

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

4,\(ab+ac+b^2+2bc+c^2\)

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

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