Найдите частное при делении многочлена \(\displaystyle 45x^{\,10}+35x^{\,8}-10x^{\,4}\) на одночлен \(\displaystyle 5x^{\,2}\) в столбик, при известном процессе деления:

\(\displaystyle -\)	\(\displaystyle \small\color{blue}{\bf 45x^{\,10}}\)	\(\displaystyle +\)	\(\displaystyle \small 35x^{\,8}\)	\(\displaystyle -\)	\(\displaystyle \small 10x^{\,4}\)	\(\displaystyle \small 5x^{\,2}\)
	\(\displaystyle \small 45x^{\,10}\)					[ ]	[ ]	[ ]
		\(\displaystyle -\)	\(\displaystyle \small\color{yellowgreen}{\bf 35x^{\,8}}\)	\(\displaystyle -\)	\(\displaystyle \small 10x^{\,4}\)
			\(\displaystyle \small 35x^{\,8}\)
				\(\displaystyle -\)	\(\displaystyle \small\color{orange}{\bf -10x^{\,4}}\)
					\(\displaystyle \small -10x^{\,4}\)
					\(\displaystyle \small0\)

С учетом найденного частного запишите разложение на множители:

\(\displaystyle 45x^{\,10}+35x^{\,8}-10x^{\,4}=5x^{\, 2}\cdot\big(\)[ ]\(\displaystyle \big){\small . }\)