Arguably the easiest way is synthetic division. We set the factor to zero and solve:
X + 3 = 0
X = -3
Next, we test it against the coefficients of the problem. If there any missing terms -- that is, a power of X not present -- list it as zero. The procedure is to drop the first coefficient, then multiply by the factor and "bounce" it up to the next line:
-3 | -3 +6 +6 +9
+9 -45 -117
-3 +15 -39 -126
The method is very fast, but not intuitive at first. Notice that we add straight down for succeeding columns, multiply by the factor, then "bounce" up to the next column again. If the final remainder is 0, it was a factor. If not, it wasn't.