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from https://answers.yahoo.com/question/index?qid=20110301123054AAIHayZ (5 years ago):
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)
