Question 1051087
change the sign of the -2 to 2 and divide

2/1===+2====-5====-6
==1=(2)=4=(8)=3==(6)0, the parentheses are the intermediate products which are added to the coefficients. You multiply each result by +2 and add.
Because the remainder is 0, it factored.
What is left is a 1===4====3
These are coefficients of a polynomial to one less power, here x^2+4x+3
That happens to factor as well (x+3)(x+1), but that isn't required to be answered here.  The polynomial factors completely, and x-2 is a factor, and x=2 is the root.
How do you remember whether to change the sign?
Use a polynomial you know, like x^2-6x+9 where the factors are (x-3)^2
The roots are x=3
If you use 3, you get a remainder of 0.