An algebraic equation (or algebraic equation of the $n$th degree with one unknown) is an equation of the form \[ x^n + a_1 x^{n-1} + a_2x^{n-2} + \cdots + a_{n-1}x + a_n = 0. \] Given the polynomial of the right hand side, we have divided through by the largest coefficient on $x^n$.
\[ x^n + a_1 x^{n-1} + a_2x^{n-2} + \cdots + a_{n-1}x + a_n = 0. \]