Find one factor of the form $x^{k}+m$, where $x^{k}$ divides the monomial with the highest power $x^{6}$ and $m$ divides the constant factor $-32$. One such factor is $x^{3}-8$. Factor the polynomial by dividing it by this factor.
$$\left(x^{3}-8\right)\left(x^{3}+4\right)$$
Consider $x^{3}-8$. Rewrite $x^{3}-8$ as $x^{3}-2^{3}$. The difference of cubes can be factored using the rule: $a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right)$.
$$\left(x-2\right)\left(x^{2}+2x+4\right)$$
Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: $x^{2}+2x+4,x^{3}+4$.
