SOLUTION: How do you factor this question and what are the steps? 12x^3 + 16x^2 – 5x – 3

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Question 1006300: How do you factor this question and what are the steps? 12x^3 + 16x^2 – 5x – 3
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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%281%2F2%2C-1%2F3%2C-3%2F2%29.

The First Two Divisions That Give Remainder 0: 

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

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

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Factorization will be whatever is equivalent to 3%28x-1%2F2%29%284x%2B6%29%28x%2B1%2F3%29.