整系数多项式在整数环上不可约性的进一步探讨

A Further Discussion of the Irreducibility of the Integer Polynomial in the Integer Ring

本文首先给出了整系数多项式有二次整系数多项式因式的一个必要条件，进而通过对整系数多项式ｆ（ｘ）＝ＡｎＸ２十αｎ－１Ｘｎ－１＋…＋αｏ中ｘｎ－２的系数αｎ－２的讨论，得到一类整系数多项式在整数环上是否可约的一个判别法。

This paper at first gives a necessary condition to the polynomial of integer coefficient which includes square factors of integer coefficient and through the discussion on the coefficient an-2ofxn-2 in the integer polynomial f(x)=anx2+an-1xn-1+…+ao obtains a criterion which proves if a kind of polynomial of integer coefficient with indices above 3 is reducible or not in the integer ring.