Разделите многочлен \(\displaystyle u^{\,4}+3u^{\,3}-22u^{\,2}+9u+9\) на многочлен \(\displaystyle u^{\,2}-4u+3\) в столбик:

\(\displaystyle -\)	\(\displaystyle \phantom{\,\,}u^{\,4}+3u^{\,3}-22u^{\,2}+9u+9\)				\(\displaystyle u^{\,2}-4u+3\)
	[ ]				[ ]
	\(\displaystyle \phantom{ xx\,} -\)	[ ]
		[ ]
		\(\displaystyle \phantom{ xxxx\,} -\)		[ ]
				[ ]
				\(\displaystyle 0\)

и запишите разложение:

\(\displaystyle u^{\,4}+3u^{\,3}-22u^{\,2}+9u+9=(u^{\,2}-4u+3)\cdot \big(\)[ ]\(\displaystyle \big).\)