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Question
Find whether the first polynomial is a factor of the second.
x + 1, 2x2 + 5x + 4
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Solution
\[ \frac{2 x^2 + 5x + 4}{x + 1}\]
\[ = \frac{2x(x + 1) + 3(x + 1) + 1}{x + 1}\]
\[ = \frac{(x + 1)(2x + 3) + 1}{(x + 1)}\]
\[ = (2x + 3) + \frac{1}{x + 1}\]
\[ \because \text{Remainder} = 1\]
\[\text{Therefore, (x + 1) is not a factor of}\ 2 x^2 + 5x + 4\]
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