Divide $(x^{2} + 5 x + 6)$ by $(x + 2)$ .

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Solution

We divide the given polynomial $x^{2} + 5 x + 6$ by the monomial $x + 2$ as shown below:

$\frac{x^{2} + 5 x + 6}{x + 2} = \frac{x^{2} + 3 x + 2 x + 6}{x + 2} = \frac{x (x + 3) + 2 (x + 3)}{x + 2} = \frac{(x + 2) (x + 3)}{x + 2} = x + 3$

Hence, $\frac{x^{2} + 5 x + 6}{x + 2} = x + 3$ .

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