Question

 phân tích đa thức thành nhân tử.
1) 3x^2 + 2x – 1
2) x^3 + 6x^2 + 11x + 6
3) x^4 + 2x^2 – 3
4) ab + ac +b^2 + 2bc + c^2
5) a^3 – b^3 + c^3 + 3abc

hộ mk cái

Answer 1

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)   \(x^3+6x^2+11x+6\)

\(=x^3+x^2+5x^2+5x+6x+6\)

\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2+5x+6\right)\)

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

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

3)   \(x^4+2x^2-3\)

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

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

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

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

4)   \(ab+ac+b^2+2bc+c^2\)

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

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

Answer 2

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, \(x^3+6x^2+11x+6\)

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

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

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

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