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Long Division Method to Divide Two Polynomials

Solve 15 y ...

Question

Solve
$(15 y^{4} + 10 y^{3} - 5 y^{2}) \div 5 y^{2}$ .

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Solution

$(15 y^{4} + 10 y^{3} - 5 y^{2}) \div 5 y^{2} = \frac{15 y^{4} + 10 y^{2} - 5 y^{2}}{5 y^{2}} = \frac{15 y^{4}}{5 y^{2}} + \frac{10 y^{3}}{5 y^{2}} - \frac{5 y^{2}}{5 y^{2}}$
$= 3 y^{2} + 2 y - 1$
Hence, $(15 y^{4} + 10 y^{3} - 5 y^{2}) \div 5 y^{2}$ is $3 y^{2} + 2 y - 1$

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