2

12(p+1) +13(p+1)+3

could this be done in quadratic form?
the the (p+1) after 12 is cubed.

Do you mean

12(p+1)^3 + 13(p+1) + 3

If so, what is the "2" on the first line supposed to contribute? Is that another exponent for the 13(p+1) term?

Quadratic generally means second degree, as in x^2. Not sure what you're after here.