Question 1206606
<br>
Note that synthetic division is a slow way to find which one of the answer choices is a root of the given polynomial; evaluating the polynomial for each of the answer choices is much faster.<br>
However, the problem is possibly intended as practice with the process of synthetic division; so let's go ahead with it.<br>
To start with, the rational roots theorem tells us the possible rational roots are 1, 2, 4, -1, -2, and -4.  Of those, -2, -1, and 1 are answer choices.<br>
With only a little experience with synthetic division, we know that trying 1 as a root makes for the easiest calculations, so we would try that answer choice first.<br>
But, assuming the problem is to give us practice using synthetic division, let's try the valid answer choices in the order they are given.<br><pre>
trying -2 as a root....

   -2 |  1  0  3 -4
      |    -2  4 -14
      +-------------
         1 -2  7 -18  the remainder is not 0; -2 is not a root

trying -1....

   -1 |  1  0  3 -4
      |    -1  1 -4
      +-------------
         1 -1  4 -8  the remainder is not 0; -2 is not a root

trying 1....

    1 |  1  0  3 -4
      |     1  1  4
      +-------------
         1  1  4  0  the remainder is 0; 1 is a root</pre>
ANSWER: 1<br>