Use the rational root theorem to find the possible rational roots. The rational roots theorem says that possible rational roots are +/- factors the constant term (36 here) divided by factors of the leading coefficient (1 here). Possible rational roots are
+/- 1, 2, 3, 4, 9, 12, 18, 36
Test each zero using the rational root test. To do this, use synthetic division to test the roots. I won't show the work here, but the roots that work are -2 and -3. As factors, this is x+2 and x+3.
From the synthetic division, we have x^2-4x+6 left over, which is irreducible.
In factored form:
f(x) = (x+2)(x+3)(x^-4x+6)
You could also use a graphing calculator to find the roots and work backwards to get the factored form too. A TI-89 Titanium would factor the polynomial and give you the above answer.
