Answer
$10r^5+2r^4+5r^2$
Work Step by Step
The long division method below shows the result of $
(90r^6+28r^5+45r^3+2r^4+5r^2)\div(9r+1)
.$
$$\begin{array}{l}
\phantom{5x-y)}10r^5+\phantom{2}2r^4\phantom{+2r^4\,\,}+\phantom{4}5r^2
\\
\color{blue}{9r+1}\color{black}{\overline{\smash{)}90r^6+28r^5+2r^4+45r^3+5r^2}}
\\
\phantom{9r+1)}\underline{90r^6+10r^5}
\\
\phantom{9r+1)90r^6+}18r^5+2r^4
\\
\phantom{9r+1)90r^6+}\underline{18r^5+2r^4}
\\
\phantom{9r+1)90r^6+18r^5+2}0+45r^3+5r^2
\\
\phantom{9r+1)90r^6+18r^5+20\,+}\underline{45r^3+5r^2}
\\
\color{red}{\phantom{9r+1)90r^6+18r^5+20\,+45r^3+5}0}
\end{array}$$Hence, the quotient is $10r^5+2r^4+5r^2$.
