Definition:Depressed Polynomial

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.