Rational root theorem. Find all the factors of the leading term's coefficient and the constant term; these are 1 and -12, respectively.
1 has only one factor: 1 (call this \(n\))
-12 has a few more: \(\pm1,\pm2,\pm3,\pm4,\pm6,\pm12\) (call these \(m\))
Potential roots will take on the form \(\dfrac mn\), which means you can check these as possible roots: \(\pm1,\pm2,\pm3,\pm4,\pm6,\pm12\)
Plug each of these into \(p(x)\). If \(p\left(\dfrac mn\right)=0\), then \(\dfrac mn\) is a root.
Unfortunately, you'll find none of these work, so this polynomial doesn't have any rational roots (which means finding any could be very tough).
