Divide the given polynomial by the given monomial:
$8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3}) \div 4 x^{2} y^{2} z^{2}$

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Solution

$8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3}) \div 4 x^{2} y^{2} z^{2}$ $= \frac{8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3})}{4 x^{2} y^{2} z^{2}}$
Taking out common factors $x^{2} y^{2} z^{2}$ in $8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3})$
$\Rightarrow$ $8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3})$ $= 8 x^{2} y^{2} z^{2} (x + y + z)$
Therefore,
$\frac{8 x^{2} y^{2} z^{2} (x + y + z)}{4 x^{2} y^{2} z^{2}} = 2 (x + y + z)$
Hence, $8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3}) \div 4 x^{2} y^{2} z^{2}$ $=$ $2 (x + y + z)$

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