Using synthetic division
1 [ 1 a b c ]
1 a + 1 a + b + 1
_________________________
1 a + 1 a + b + 1 a + b + c + 1 = 14
Which means that
a + b + c = 13
And
-1 [ 1 a b c ]
-1 1 - a a - b - 1
____________________________
1 a -1 -a + b + 1 a - b + c - 1 = 0
Which means that
a - b + c = 1
And
-2 [ 1 a b c ]
-2 -2a + 4 4a -2b -8
_____________________________
1 a -2 -2a + b + 4 4a - 2b + c - 8 = -18
Which means that
4a - 2b + c = -10
So we have this system
a + b + c =13
a - b + c = 1
4a - 2b + c = -10
Subtract the second equation from the first
2b = 12
b = 6
So the last two equations become
a - 6 + c = 1 ⇒ a + c = 7 ( 1)
4a - 2(6) + c = -10 ⇒ 4a + c = 2 ⇒ -4a - c = -2 (2)
Add (1) and (2) and we get that
-3a = 5
a = -5/3
And
-5/3 + c = 21/3
c = 26/3
See the graph here : https://www.desmos.com/calculator/5x7foeorus