Question 1006300
Rational Roots theorem and synthetic division.
The possible roots to try are the negative and positive of 1,3,1/3,1/2,3/2.


You will find none of the integer values will work as roots.


Skipping any showing of the process, the roots that work are {{{system(1/2,-1/3,-3/2)}}}.


The First Two Divisions That Give Remainder 0:


<pre>
      |     12       16       -5       -3
-1/3 |               -4       -4       3
      |_______________________________________
           12       12       -9        0

</pre>
Next remove the factor of 3 to make the next synthetic division easier, but remember the factor for later.
<pre>
      |      4        4       -3
 1/2 |                2        3
      |_______________________________________
            4         6        0
</pre>

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Factorization will be whatever is equivalent to {{{3(x-1/2)(4x+6)(x+1/3)}}}.