Question

Phân tích Đa thức thành nhân tử 

1)3x^3-12x

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

X^2 -7xy+10y^2

 

Answer 1

1) \(3x^3-12x\)

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

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

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

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

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

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

3) \(x^2-7xy+10y^2\)

\(=\left(x^2-2xy\right)-\left(5xy-10y^2\right)\)

\(=x\left(x-2y\right)-5y\left(x-2y\right)\)

\(=\left(x-5y\right)\left(x-2y\right)\)

Answer 2

1) \(3x^3-12x\)

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

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

2) \(x^3+x^2-x-1\)

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

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

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

Answer 3

1)   \(3x^3-12x\)

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

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

2)     \(x^3+x^2-x-1\)

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

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

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

3)      \(x^2-7xy+10y^2\)

\(=\left(x^2-2xy\right)-\left(5xy-10y^2\right)\)

\(=x\left(x-2y\right)-5y\left(x-2y\right)\)

\(=\left(x-2y\right)\left(x-5y\right)\)