Divide the given polynomial by the given monomial. $(3 y^{8} - 4 y^{6} + 5 y^{4}) \div y^{4}$

3 y^{4} - 4 y^{2} + 5

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3 y^{3} - 4 y^{2} - 5

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3 y^{3} - 4 y^{2} + 5

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3 y^{4} - y^{2} + 5

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Solution

The correct option is A $3 y^{4} - 4 y^{2} + 5$ .
Now, $(3 y^{8} - 4 y^{6} + 5 y^{4}) \div y^{4}$
$= \frac{3 y^{8} - 4 y^{6} + 5 y^{4}}{y^{4}}$
$= \frac{3 y^{8}}{y^{4}} - \frac{4 y^{6}}{y^{4}} + \frac{5 y^{4}}{y^{4}}$
$= 3 y^{8 - 4} - 4 y^{6 - 4} + 5 y^{4 - 4}$ [ $\frac{a^{m}}{a^{n}} = a^{m - n}, a \neq 0$ ]
$= 3 y^{4} - 4 y^{2} + 5$

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