Найдите частное при делении многочлена \(\displaystyle t^{\,17}-12t^{\,8}+30t^{\,7}\) на одночлен \(\displaystyle t^{\,4}\) в столбик при известном процессе деления:

\(\displaystyle -\)	\(\displaystyle \small\color{blue}{\bf t^{\,17}}\)	\(\displaystyle -\)	\(\displaystyle \small 12t^{\,8}\)	\(\displaystyle +\)	\(\displaystyle \small 30t^{\,7}\)	\(\displaystyle \small t^{\,4}\)
	\(\displaystyle \small t^{\,17}\)					[ ]	[ ]	[ ]
		\(\displaystyle -\)	\(\displaystyle \small\color{yellowgreen}{\bf -12t^{\,8}}\)	\(\displaystyle +\)	\(\displaystyle \small 30t^{\,7}\)
			\(\displaystyle \small -12t^{\,8}\)
				\(\displaystyle -\)	\(\displaystyle \small\color{orange}{\bf 30t^{\,7}}\)
					\(\displaystyle \small 30t^{\,7}\)
					\(\displaystyle \small0\)

С учетом найденного частного запишите разложение на множители:

\(\displaystyle t^{\,17}-12t^{\,8}+30t^{\,7}=t^{\, 4}\cdot \big(\)[ ]\(\displaystyle \big){\small . }\)