Question

3, phân tích đa thức thành nhân tử 

a, x^3-x^2+2                          b, 2x^2-5xy+2y^2

c, x^2 +3xy+2y^2

Answer 1

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

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

b: \(=2x^2-4xy-xy+2y^2\)

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

c: \(=\left(x+y\right)\left(x+2y\right)\)

Answer 2

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

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

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