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Question
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
10x2 − 7x + 8, 5x − 3
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Solution
\[ \frac{10 x^2 - 7x + 8}{5x - 3}\]
\[ = \frac{2x(5x - 3) - \frac{1}{5}(5x - 3) + \frac{47}{5}}{(5x - 3)}\]
\[ = \frac{(5x - 3)(2x - \frac{1}{5}) + \frac{47}{5}}{(5x - 3)}\]
\[ = (2x - \frac{1}{5}) + \frac{\frac{47}{5}}{5x - 3}\]
\[\text{Therefore,} \]
\[\text{quotient }= 2x - \frac{1}{5} \text{and remainder} = \frac{47}{5} . \]
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