Consider $x^{4}-40x^{2}+144$. 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 $144$. One such factor is $x^{2}-36$. Factor the polynomial by dividing it by this factor.
$$\left(x^{2}-36\right)\left(x^{2}-4\right)$$
Consider $x^{2}-36$. Rewrite $x^{2}-36$ as $x^{2}-6^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(x-6\right)\left(x+6\right)$$
Consider $x^{2}-4$. Rewrite $x^{2}-4$ as $x^{2}-2^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
