Itw's given that - 2 is a zero

Using synthetic division, we get:

  - 2| 1    7    4  - 12 
     |_____-2 - 10    12  
       1    5  - 6     0

Since - 2 is a zero, then x = - 2, and x + 2 = 0, so x + 2 is a factor

We now get: 

 ------- Factoring 



Therefore, 


If x - 2 is a factor, then x - 2 = 0, and so, x = 2 (one of the zeroes)

If x - 2 is a factor, then 2 (one of the zeroes) should NOT produce a remainder when the Remainder theorem: is used.

Remainder theorem: 

Therefore, we get: 
 




With f(2) = 32, a remainder exists, and so, x - 2 is NOT a factor