Question 221774
If (x-1) is a factor of {{{3x^3+x^2+2kx+4}}} then it will divide into it evenly. So we will use Synthetic Division to solve this:
<pre>
1 |    3   1   2k       4
---        3   4     2k+4
       ------------------
       3   4   2k+4  2k+8
</pre>
The remainder, we can see above, is 2k+8. Since we know that (x-1) divides evenly, the remainder must be zero:
2k+8 = 0
Now we solve this for k. Subtract 8 from both sides:
2k = -8
Divide both sides by 2:
k =  -4