Answer is 0
P(x) = ƒ(x3) + xg(x3)
P(1) = ƒ(1) + g(1) ...(1)
Now P(x) is divisible by x2 + x + 1
⇒ P(x) = Q(x)(x2 + x + 1)
P(w) = 0 = P(w2) where w, w2 are non-real cube roots of units
P(x) = ƒ(x3) + xg(x3)
P(w) = ƒ(w3) + wg(w3) = 0
ƒ(1) + wg(1) = 2 ...(2)
P(w2) = ƒ(w6) + w2g(w6) = 0
ƒ(1) + w2g(1) = 0 ...(3)
(2) + (3)
⇒ 2ƒ(1) + (w + w2)g(1) = 0
2ƒ(1) = g(1) ...(4)
(2) – (3)
⇒ (w – w2)g(1) = 0
g(1) = 0 = ƒ(1) from (4)
from (1) P(1) = ƒ(1) + g(1) = 0