Задание
Найдите частное при делении многочлена \(\displaystyle -33x^{\,9}+6x^{\,8}-3x^{\,4}\) на одночлен \(\displaystyle -3x^{\,3}\) в столбик при известном процессе деления:
\(\displaystyle -\) | \(\displaystyle \small\color{blue}{\bf -33x^{\,9}}\) | \(\displaystyle +\) | \(\displaystyle \small 6x^{\,8}\) | \(\displaystyle -\) | \(\displaystyle \small 3x^{\,4}\) | \(\displaystyle \small -3x^{\,3}\) | ||
\(\displaystyle \small -33x^{\,9}\) | [ ] | [ ] | [ ] | |||||
\(\displaystyle -\) | \(\displaystyle \small\color{yellowgreen}{\bf 6x^{\,8}}\) | \(\displaystyle -\) | \(\displaystyle \small 3x^{\,4}\) | |||||
\(\displaystyle \small 6x^{\,8}\) | ||||||||
\(\displaystyle -\) | \(\displaystyle \small\color{orange}{\bf -3x^{\,4}}\) | |||||||
\(\displaystyle \small -3x^{\,4}\) | ||||||||
\(\displaystyle \small0\) |
С учетом найденного частного запишите разложение на множители:
\(\displaystyle -33x^{\,9}+6x^{\,8}-3x^{\,4}=-3x^{\, 3}\cdot\big(\)[ ]\(\displaystyle \big){\small . }\)