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 [tex]n[/tex])
-12 has a few more: [tex]\pm1,\pm2,\pm3,\pm4,\pm6,\pm12[/tex] (call these [tex]m[/tex])
Potential roots will take on the form [tex]\dfrac mn[/tex], which means you can check these as possible roots: [tex]\pm1,\pm2,\pm3,\pm4,\pm6,\pm12[/tex]
Plug each of these into [tex]p(x)[/tex]. If [tex]p\left(\dfrac mn\right)=0[/tex], then [tex]\dfrac mn[/tex] 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).
