Consider $x^{4}-2x^{2}+1$. Find one factor of the form $x^{k}+m$, where $x^{k}$ divides the monomial with the highest power $x^{4}$ and $m$ divides the constant factor $1$. One such factor is $x^{2}-1$. Factor the polynomial by dividing it by this factor.
$$\left(x^{2}-1\right)\left(x^{2}-1\right)$$
Consider $x^{2}-1$. Rewrite $x^{2}-1$ as $x^{2}-1^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
