Răspuns:
#N (n + 1) (n + 2) (n + 4) # sau # N ^ 4 + 7N ^ 3 ^ 2 + 14n + 8n #
Explicaţie:
# 30 + 114 * (n-1) +81 (n-1) (n-2) +17 (n-1) (n-2) (n-3) + (n-1) (n-2) (n-3) (n-4) #
După utilizare # Y = n-1 # transformat, acest polinom a devenit
# 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 + 41y ^ 2 + 61y + 30 #
=# (N-1) ^ 4 + 11 (n-1) ^ 3 + 41 (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 + 7N ^ 2 + 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) #
