a ) \(x^3-3x^2-4x+12\)
\(=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x^2-4\right)\left(x-3\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x-3\right)\)
b ) \(x^4-5x^2+4\)
Đặt \(x^2=t.\)
Ta có : \(t^2-5t+4\)
\(=t^2-t-4t+4\)
\(=\left(t-4\right)\left(t-1\right)\)
hay : \(\left(x^2-4\right)\left(x^2-1\right)\)
\(=\left(x-2\right)\left(x+1\right)\left(x-1\right)\left(x+1\right)\)
\(=\left(x+1\right)^2\left(x-1\right)\left(x-2\right)\)
c ) \(\left(x+y+z\right)^3-x^3-y^3-z^3\)
\(=x^3+y^3+z^3+3xy+3yz+3zx-x^3-y^3-z^3\)
\(=3\left(xy+yz+zx\right)\)
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