Cevap:
# n (n + 1) (n + 2), (n + 4) # veya # N ^ 4 + 7n ^ 3 + 14n ^ 2 + 8n #
Açıklama:
30. + 114 * (n-1) +81 (n-1) (n-2) + 17 (n-1) (n-2) (n-3) + (n-1) (n-2) (n-3) (n-4) #
Kullandıktan sonra • y = n-1 # dönüşüm, bu polinom oldu
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 + 61n-61 + 30 #
=# N ^ 4 + 7n ^ 3 + 14n ^ 2 + 8n #
=# N * (n ^ 3 + 7n ^ 2 + 14n + 8) #
=# N * (n ^ 2 + n + 6n ^ 6n + 2 + 8n + 8) #
=# N * (n + 1) * (n ^ 6n + 2 + 8) #
=# n (n + 1) (n + 2), (n + 4) #
