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Question
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
y4 + y2, y2 − 2
Solution
\[\frac{y^4 + y^2}{y^2 - 2}\]
\[ = \frac{y^2 ( y^2 - 2) + 3( y^2 - 2) + 6}{y^2 - 2}\]
\[ = \frac{( y^2 - 2)( y^2 + 3) + 6}{y^2 - 2}\]
\[ = ( y^2 + 3) + \frac{6}{y^2 - 2}\]
\[\text{Therefore, quotient} = y^2 + 3 \text{and remainder} = 6 .\]
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