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Question
Find whether the first polynomial is a factor of the second.
4y + 1, 8y2 − 2y + 1
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Solution
\[\frac{{8y}^2 -2y+1}{4y+1}\]
\[ = \frac{2y (4y+1)-1(4y+1)+2}{4y+1}\]
\[ = \frac{(4y+1)(2y-1)+2}{4y+1}\]
\[ = (2y-1)+ \frac{2}{4y+1}\]
\[ \because \text{Remainder = 2}\]
\[ \therefore \text{( 4y+1) is not a factor of}\ {8y}^2 -2y+1.\]
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