Odgovor:
#N (n + 1) (n + 2) (n + 4) # ili # N ^ 4 + 7n ^ 3 + 2 + 14n ^ 8n #
Obrazloženje:
# 30 + 114 * (n-1) 81 (n-1), (n-2) +17 (n-1), (n-2), (n-3) + (n-1), (n-2) (n-3) (n-4) *
Nakon upotrebe # Y = n-1 # transformacije, taj polinom postao
# 30 + + 114y 81y (y-1) + 17y (y-1), (y-2) + y (y-1), (y-2), (y-3) *
=# 30 + + 114y 81y ^ 2-81y + 17 * (y ^ 3-3y ^ 2 + 2y) + (y ^ 2y) + (y ^ 2-5y + 6) #
=# 30 + 81y ^ 2 + 33y + 17y ^ 3-51y ^ 2 + 34y + y ^ 4-6y ^ 3 + 11y ^ 2-6y #
=# Y ^ 4 + 11y ^ 3 ^ 2 + 41y + 61y + 30 #
=# (N-1) ^ 4 + 11 (n-1) + 41 ^ 3 (n-1) ^ 2 * 61 + (n-1) + 30 #
=# N ^ 4-4n ^ 3 ^ + 6n 2-4n + 1 + 11n ^ 3-33n ^ 2 + 33n-11 + 41n ^ 2-82n + 41 + 61 + 61n-30 #
=# N ^ 4 + 7n ^ 3 + 2 + 14n ^ 8n #
=# * N (n ^ 3 + 2 + 7n ^ 14n + 8) #
=# * N (n ^ 2 + n + 6n + 2 ^ 6n + 8n + 8) #
=# * N (n + 1) + (n ^ 2 + 6n + 8) #
=#N (n + 1) (n + 2) (n + 4) #
