Question 1193950
use 2synthetic division as shown below:


<img src = "http://theo.x10hosting.com/2022/050302.jpg" >


the last position in the synthetic division is 2k + 14.
if x - 2 is a factor of the equation, then 2k + 14 must be equal to 0.
solve for k to get k = -7.


here's a reference on synthetic division.
<a href = "https://www.purplemath.com/modules/synthdiv.htm" target = "_blank">https://www.purplemath.com/modules/synthdiv.htm</a>


replacing k in the original equation with -7, i get:
y = x^4 -2x^2 -7x + 6
the graph of that equation below shows that one of the zeroes of that equation is at x = 2.
the factor is (x - 2).


<img src = "http://theo.x10hosting.com/2022/050301.jpg" >