## Algebraic integers may be the roots of nonmonic primitive polynomials

Show that an algebraic integer may be expressed as a root of a nonmonic primitive polynomial.

Certainly the roots of $x^2+1$ are algebraic integers (namely, $\pm i$). Consider $(x^2+1)(2x+3) = 2x^3 + 3x^2 + 2x + 3$; this polynomial is primitive and nonmonic, and has $\pm i$ as roots.