Book One SECTION I About complete polynomials and complete equations (29.) Any polynomial that contains only one unknown x can be repre- sented in general by ax T + bx T -1 + cx T -2 · · · + s, where T is the highest degree of x and a, b, c, etc. are arbitrary coefficients. Likewise, any equation in one unknown can generally be represented by ax T + bx T -1 + cx T -2 + · · · + s = 0. However, the large number of terms that can enter polynomials and equa- tions, as their degree and the number of unknowns increases, requires us to represent these as compactly as possible. We first present the various notations that we propose to use. (30.) We represent any polynomial in one unknown by the abbreviated expression (x) T , which means a polynomial in one unknown, with degree T . Likewise, we represent any equation in one unknown x by the abbreviated expression (x) T = 0. The number of terms of such a polynomial or equation is written N (x) T . (31.) A complete polynomial is defined as a polynomial that contains all