Задание
Найдите частное при делении многочлена \(\displaystyle 15t^{\,13}+10t^{\,6}\) на одночлен \(\displaystyle t^{\,5}\) в столбик при известном процессе деления:
| \(\displaystyle -\) | \(\displaystyle \small\color{blue}{\bf 15t^{\,13}}\) | \(\displaystyle +\) | \(\displaystyle \small 10t^{\,6}\) | \(\displaystyle \small t^{\,5}\) | |
\(\displaystyle \small 15t^{\,13}\) | [ ] | [ ] | |||
| \(\displaystyle -\) | \(\displaystyle \small \color{yellowgreen}{\bf 10t^{\,6}}\) | ||||
\(\displaystyle \small 10t^{\,6}\) | |||||
| \(\displaystyle \small 0\) | |||||
С учетом найденного частного запишите разложение на множители:
\(\displaystyle 15t^{\,13}+10t^{\,6}=t^{\,5}\cdot \big(\)[ ]\(\displaystyle \big){\small . }\)