\begin{array}{c|c c c c|c}
 & 10 & 321 & 632 & 60+20k & 2k\\
-^1/_{10} & & -1 & -32 & -60 & -2k \\
\hline
 & 10 & 320 & 600 & 20k & 0 \\
\end{array}

\\
10 x^4 + 321 x^3 + 632 x^2 + (60+20k)x + 2k = \\
\left (x + \frac{1}{10}\right)(10 x^3 + 320x^2 + 600x + 20k) = \\
(10x+1)(x^3 + 32x^2 + 60x + 2k)

\\
\frac{k(20x +2)}
{10 x^4 + 321 x^3 + 632 x^2 + (60+20k)x + 2k} = \\
\frac{2k(10x+1)}
{(10x+1)(x^3 + 32x^2 + 60x + 2k)} = \\
\frac{2k}{x^3 + 32x^2 + 60x + 2k}

x^3 + 32x^2 + 60x = x(x^2+32x+60)

x_{1,2} = -16 \pm \sqrt{256-60} = -16 \pm \sqrt{196} = -16 \pm 14 = \left\{\begin{matrix}
-2 \\
-30
\end{matrix}\right.

x^2+32x+60 = (x+2)(x+30)

\frac{2k}{x^3 + 32x^2 + 60x + 2k} = \frac{2k}{x(x+2)(x+30) + 2k}