Задание
Найдите частное при делении многочлена \(\displaystyle -77z^{\,11}+49z^{\,7}-7z^{\,5}\) на одночлен \(\displaystyle 7z^{\,3}\) в столбик, при известном процессе деления:
| \(\displaystyle -\) | \(\displaystyle \small\color{blue}{\bf -77z^{\,11}}\) | \(\displaystyle +\) | \(\displaystyle \small 49z^{\,7}\) | \(\displaystyle -\) | \(\displaystyle \small 7z^{\,5}\) | \(\displaystyle \small 7z^{\,3}\) | ||
\(\displaystyle \small -77z^{\,11}\) | [ ] | [ ] | [ ] | |||||
| \(\displaystyle -\) | \(\displaystyle \small\color{yellowgreen}{\bf 49z^{\,7}}\) | \(\displaystyle -\) | \(\displaystyle \small 7z^{\,5}\) | |||||
\(\displaystyle \small 49z^{\,7}\) | ||||||||
| \(\displaystyle -\) | \(\displaystyle \small\color{orange}{\bf -7z^{\,5}}\) | |||||||
\(\displaystyle \small -7z^{\,5}\) | ||||||||
| \(\displaystyle \small0\) | ||||||||
С учетом найденного частного запишите разложение на множители:
\(\displaystyle -77z^{\,11}+49z^{\,7}-7z^{\,5}=7z^{\, 3}\cdot\big(\)[ ]\(\displaystyle \big){\small . }\)