# A Difficult Factoring Problem

The following algebraic expression looks like a mess with no immediately obvious way to factor it. The instructions are to factor  $m+\left({m}^{2}-m-12\right){x}^{2}-\left(2\,{m}^{2}-4\right)x+{m}^{2}$

However if we gather our wits, we observe that the expression can be thought of a quadratic equation in the variable x, i.e.

$m+\left({m}^{2}-m-12\right){x}^{2}-\left(2\,{m}^{2}-4\right)x+{m}^{2}=0$

Note that ${m}^2+m$ will behave as the “c” that you will substitute into the quadratic formula.

Finally the two zeros obtained from the quadratic equation will correspond to two distinct factors by the factor theorem.