Задание
Найдите частное при делении многочлена \(\displaystyle -44z^{\,14}-121z^{\,12}+77z^{\,9}\) на одночлен \(\displaystyle -11z^{\,7}\) в столбик при известном процессе деления:
| \(\displaystyle -\) | \(\displaystyle \small\color{blue}{\bf -44z^{\,14}}\) | \(\displaystyle -\) | \(\displaystyle \small 121z^{\,12}\) | \(\displaystyle +\) | \(\displaystyle \small 77z^{\,9}\) | \(\displaystyle \small -11z^{\,7}\) | ||
\(\displaystyle \small -44z^{\,14}\) | [ ] | [ ] | [ ] | |||||
| \(\displaystyle -\) | \(\displaystyle \small\color{yellowgreen}{\bf -121z^{\,12}}\) | \(\displaystyle +\) | \(\displaystyle \small 77z^{\,9}\) | |||||
\(\displaystyle \small -121z^{\,12}\) | ||||||||
| \(\displaystyle -\) | \(\displaystyle \small\color{orange}{\bf 77z^{\,9}}\) | |||||||
\(\displaystyle \small 77z^{\,9}\) | ||||||||
| \(\displaystyle \small0\) | ||||||||
С учетом найденного частного запишите разложение на множители:
\(\displaystyle -44z^{\,14}-121z^{\,12}+77z^{\,9}=-11z^{\, 7}\cdot\big(\)[ ]\(\displaystyle \big){\small . }\)