n3 + 3n2 + 4n + 12 = (n3 + 3n2) + (4n + 12)
= n2(n + 3) + 4(n + 3)
= (n2 + 4)(n + 3).
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-4n3 + 8n2 - 4n + 7
Given any number it is easy to find a rule based on a polynomial of order 4 such that the four numbers are as listed in the question and the next is the given number. There are also non-polynomial solutions.The polynomial with the lowest order for this sequence isUn = -3n2 + 14n + 64 for n = 1, 2, 3, ...and, accordingly, the next number is 59.
3n2-8n+4 = (3n-2)(n-2) when factored
3
The GCF is 3n.