You're on the right track by using synthetic division. But the value on in the box should be -1, since x+1=0 x=-1 is your zero
-1 | 2 1 -2 -1
_____________
2 <---------bring down the first term
-1 | 2 1 -2 -1
__-2___________ Place the product of (-1) and 2 under the 1
2 -1 Add the terms
-1 | 2 1 -2 -1
__-2___1________ Place the product of (-1) and (-1) under the -2
2 -1 -1 Add the terms
-1 | 2 1 -2 -1
__-2___1___1_____ Place the product of (-1) and (-1) under the -2
2 -1 -1 0 Add the terms
Since you get a remainder of 0 it shows that x+1 is a zero (which was already given, but we proved it). The qoutient coefficients 2 -1 -1 are then placed next to variables.
So this is your factor
If you multiplied by you would get
So this is your factored form and your answer.
Hope this helps.