Antwoord:
#n (n + 1) (n + 2) (n + 4) # of # N ^ 4 ^ 7n + 3 + 14n ^ 2 + 8n #
Uitleg:
# 30 + 114 * (n-1) 81 (n-1) (n-2) 17 (n-1) (n-2) (n-3) + (n-1) (n-2) (n-3) (n-4) #
Na gebruik # Y = n-1 # transformatie, deze polynoom werd
# 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 ^ 3 + 4-4n 6n ^ 2-4n + 1 + 11n ^ 3-33n ^ 2 + 33n-11 + 41 n ^ 2-82n + 41 + 61 + 61N-30 #
=# N ^ 4 ^ 7n + 3 + 14n ^ 2 + 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) #
