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Divide Polynomials by Monomials

Divide: $\quad 5x^{3}y + 35x^{2}y^{2} - 10x\quad$ by $\quad x + 2$

(1) $\begin{equation*} \frac{5x^{3}y + 35x^{2}y^{2} - 10x}{5x}$ \end{equation*}$

Separate the terms of our polynomial and cancel where needed

(2) $\begin{equation*} \frac{5x^{3}y}{5x} + \frac{35x^{2}y^{2}}{5x} - \frac{10x}{5x} \end{equation*}$

(3) $\begin{equation*} \frac{x^{3}y}{x} + \frac{7x^{3}y^{2}}{x} - \frac{-2x}{x} \end{equation*}$

(4) $\begin{equation*} \boxed{x^{2}y + 7xy^{2} - 2} \end{equation*}$