Question

Phân tích đa thức thành nhân tử:

a) \(x^2-4+\left(x-2\right)^2\)

b) \(x^3+2x^2+x+2\)

c) \(x^3-2x^2+x-xy^2\)

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

Giúp mình với. Mình cần gấp lắm! Cảm ơn trước!!!

Answer 1

a ) \(x^2-4+\left(x-2\right)^2\)

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

\(=2x^2-4x\)

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

b ) \(x^3+2x^2+x+2\)

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

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

c ) \(x^3-2x^2+x-xy^2\)

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

\(=x\left[\left(x-1\right)^2-y^2\right]\)

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

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

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

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

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