\input zb-basic \input zb-matheduc \iteman{ZMATH 2011a.00729} \itemau{Donnell, William A.} \itemti{Elementary theory of factoring trinomials with integer coefficients over the integers.} \itemso{Int. J. Math. Educ. Sci. Technol. 41, No. 8, 1114-1121 (2010).} \itemab Summary: An important component of intermediate and college algebra courses involves teaching students methods to factor a trinomial with integer coefficients over the integers. The aim of this article is to present a theoretical justification of that which is often taught, but really never explained as to why it works. The theory is presented, and a suggestion for an inquiry-based learning project is given. \itemrv{~} \itemcc{H24 H34 F64} \itemut{factoring trinomials over the integers; middle term splitting method; intermediate algebra; college algebra; elementary number theory; inquiry-based learning (R.L. Moore); quadratic equations} \itemli{doi:10.1080/0020739X.2010.500699} \end