Question

Phân tích các đa thức sau thành nhân tử:

a) x⁴+2x³-4x-4

b)x²(y-z)+y²(z-x)+z²(x-y)

Answer 1

b)\(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)

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

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

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

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

\(=\left(x-y\right)\left(z^2+xy-zy-zx\right)\)

\(=\left(x-y\right)\left[z\left(z-x\right)-y\left(z-x\right)\right]\)

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