$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+4;}{\phantom{;}x^{3}+3x^{2}-12x\phantom{;}+42\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+4\overline{\smash{)}\phantom{;}x^{4}+7x^{3}\phantom{-;x^n}-6x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+4;}\underline{-x^{4}-4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-4x^{3};}\phantom{;}3x^{3}\phantom{-;x^n}-6x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n;}\underline{-3x^{3}-12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{3}-12x^{2}-;x^n;}-12x^{2}-6x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n-;x^n;}\underline{\phantom{;}12x^{2}+48x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}12x^{2}+48x\phantom{;}-;x^n-;x^n;}\phantom{;}42x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n-;x^n-;x^n;}\underline{-42x\phantom{;}-168\phantom{;}\phantom{;}}\\\phantom{;;;-42x\phantom{;}-168\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-166\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+3x^{2}-12x+42+\frac{-166}{x+4}$