posted by ladybug .
use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
The RZT says that any rational root will be a factor of 22. So, the number of possibilities is quite limited:
±1 ±2 ±11 ±22
A little synthetic division shows that
f(x) = (x-11)(x+1)(x+2)