How to factorize this cubic equation? In one of the mathematics book, the author factorized following term
$$x^3 - 6x + 4 = 0$$
to
$$( x - 2) ( x^2 + 2x -2 ) = 0.$$
How did he do it?

The rational root theorem gives a list of all possible rational roots of a polynomial with integer coefficients that have a given leading coefficient and a given constant coefficient. In this case, the leading coefficient is $1$ and the constant coefficient is $4.$ The theorem tells us that all rational roots are in the set $\left\{ \pm\dfrac 1 1, \pm\dfrac 2 1, \pm \dfrac 4 1 \right\},$ the numerator being in this the only divisor of the leading coefficient $1$ and the denominators being the divisors of the constant coefficient $4$. That doesn't mean there are rational roots; it only means there are not any that don't belong to this set. There are only six members of this set, so it's easy to plug in all of them and see if you get $0$. When you plug in $2$, you get $0$, so there's your factorization.
