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

2 (x - y + z)

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2 (x + y - z)

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2 (x + y + z)

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4 (x + y + z)

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Solution

The correct option is C $2 (x + y + z)$
$8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3}) \div 4 x^{2} y^{2} z^{2}$
$= \frac{8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3})}{4 x^{2} y^{2} z^{2}}$
$= \frac{8 x^{2} y^{2} z^{2} (x + y + z)}{4 x^{2} y^{2} z^{2}}$
$= 2 (x + y + z)$

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