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Question
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
3x2 + 4x + 5, x − 2
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Solution
\[\frac{3 x^2 + 4x + 5}{x - 2}\]
\[ = \frac{3x(x - 2) + 10(x - 2) + 25}{(x - 2)}\]
\[ = \frac{(x - 2)(3x + 10) + 25}{(x - 2)}\]
\[ = (3x + 10) + \frac{25}{(x - 2)}\]
\[\text{Therefore,} \]
\[\text{quotient = 3x + 10 and remainder = 25 .} \]
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