Definition:Depressed Polynomial

Definition
Let $P_n \left({x}\right)$ be a polynomial in $x$:
 * $P_n \left({x}\right) = a_n x^n + a_{n-1} x^{n-1} + a_{n-2} x^{n-2} + \cdots + a_1 x + a_0$

By adding $a_n \left({x + \frac {a_{n-1}} n}\right)^n$ to both sides of the equation $P_n \left({x}\right) = 0$, one can obtain a polynomial:
 * $P_n \left({y}\right) = y^n + b_{n-2} y^{n-2} + \cdots + b_1 y + b_0$.

where $y = x + \frac {a_{n-1}} n$.

This new polynomial has the same roots as $P_n \left({x}\right)$ shifted by $\frac {a_{n-1}} n$.

Such a polynomial with the highest but one term absorbed is called a depressed polynomial.

Some authors have jocularly suggested that polynomials with more than one of the terms absorbed might be referred to as "downright despondent".

Note
The substitution $y = x + \frac {a_{n-1}} n$ is known as a Tschirnhaus Transformation.