בניגוד לחילוק ארוך ללא פרמטרים, בו אנו בודקים כמה פעמים נכנס המספר השמאלי בימני, בחילוק ארוך עם פרמטרים אנו מחלקים את הפרמטרים עם החזקה הגדולה ביותר מימין בשמאל. למשל, בתרגיל
2
x
4
+
4
x
3
+
2
x
2
−
8
x
+
2
{\displaystyle {\frac {2x^{4}+4x^{3}+2x^{2}-8}{x+2}}}
2
x
4
{\displaystyle \ 2x^{4}}
x
{\displaystyle \ x}
2
x
3
{\displaystyle \ 2x^{3}}
2
x
3
_
2
x
4
+
4
x
3
+
2
x
2
−
8
¯
⌉
x
+
2
{\displaystyle {\begin{matrix}2x^{3}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\{\underline {\ }}{\overline {2x^{4}+4x^{3}+2x^{2}-8}}{\big \rceil }{x+2}&\ \end{matrix}}}
עתה נכפיל את התוצאה במספר משמאל ונחסיר אותה מהמספר שבימין :
2
x
3
_
2
x
4
+
4
x
3
+
2
x
2
−
8
¯
⌉
x
+
2
−
2
x
4
+
4
x
3
_
=
=
{\displaystyle {\begin{matrix}2x^{3}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\{\underline {\ }}{\overline {2x^{4}+4x^{3}+2x^{2}-8}}{\big \rceil }{x+2}&\ \\{\underline {\ -2x^{4}+4x^{3}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ =\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{matrix}}}
2
x
3
_
2
x
4
+
4
x
3
+
2
x
2
−
8
¯
⌉
x
+
2
−
2
x
4
+
4
x
3
_
=
=
2
x
2
−
8
{\displaystyle {\begin{matrix}2x^{3}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\{\underline {\ }}{\overline {2x^{4}+4x^{3}+2x^{2}-8}}{\big \rceil }{x+2}&\ \\{\underline {\ -2x^{4}+4x^{3}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ =\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,2x^{2}-8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{matrix}}}
עתה נחזור על הפעולות; נחלק שוב את החזקה הגבוה ביותר מימין (
2
x
2
{\displaystyle 2x^{2}}
x
{\displaystyle x}
2
x
{\displaystyle 2x}
2
x
3
+
2
x
_
2
x
4
+
4
x
3
+
2
x
2
−
8
¯
⌉
x
+
2
−
2
x
4
+
4
x
3
_
=
=
2
x
2
−
8
{\displaystyle {\begin{matrix}2x^{3}+2x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\{\underline {\ }}{\overline {2x^{4}+4x^{3}+2x^{2}-8}}{\big \rceil }{x+2}&\ \\{\underline {\ -2x^{4}+4x^{3}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ =\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,2x^{2}-8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{matrix}}}
נכפיל את התוצאה ונחסירה מהמספר מימין :
2
x
3
+
2
x
_
2
x
4
+
4
x
3
+
2
x
2
−
8
¯
⌉
x
+
2
−
2
x
4
−
4
x
3
_
=
=
2
x
2
−
8
−
2
x
2
−
4
x
_
−
4
x
−
8
{\displaystyle {\begin{matrix}2x^{3}+2x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\{\underline {\ }}{\overline {2x^{4}+4x^{3}+2x^{2}-8}}{\big \rceil }{x+2}&\ \\{\underline {\ -2x^{4}-4x^{3}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ =\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,2x^{2}-8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\underline {-2x^{2}-4x}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-4x-8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{matrix}}}
נחלק
−
4
x
{\displaystyle \ -4x}
x
{\displaystyle \ x}
4
{\displaystyle 4}
2
x
3
+
2
x
−
4
_
2
x
4
+
4
x
3
+
2
x
2
−
8
¯
⌉
x
+
2
−
2
x
4
−
4
x
3
_
=
=
2
x
2
−
8
−
2
x
2
−
4
x
_
−
4
x
−
8
{\displaystyle {\begin{matrix}2x^{3}+2x-4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\{\underline {\ }}{\overline {2x^{4}+4x^{3}+2x^{2}-8}}{\big \rceil }{x+2}&\ \\{\underline {\ -2x^{4}-4x^{3}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ =\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,2x^{2}-8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\underline {-2x^{2}-4x}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-4x-8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{matrix}}}
נכפיל את התוצאה
−
4
{\displaystyle \ -4}
x
+
2
{\displaystyle \ x+2}
2
x
3
+
2
x
−
4
_
2
x
4
+
4
x
3
+
2
x
2
−
8
¯
⌉
x
+
2
−
2
x
4
−
4
x
3
_
=
=
2
x
2
−
8
−
2
x
2
−
4
x
_
−
4
x
−
8
−
(
−
4
x
−
8
)
_
{\displaystyle {\begin{matrix}2x^{3}+2x-4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\{\underline {\ }}{\overline {2x^{4}+4x^{3}+2x^{2}-8}}{\big \rceil }{x+2}&\ \\{\underline {\ -2x^{4}-4x^{3}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ =\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,2x^{2}-8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\underline {-2x^{2}-4x}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-4x-8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\underline {-(-4x-8)}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\end{matrix}}}
אין שארית ולכן הפתרון הוא :
2
x
3
+
2
x
−
4
{\displaystyle \ 2x^{3}+2x-4}
במידה ויש שארית נרשום אותה וכמובן נזכור לחלק אותה במכנה (לדוגמה אם השארית הייתה שתים הינו מוספים את האיבר
2
x
+
2
{\displaystyle {\frac {2}{x+2}}}
