Divide : $a^{2} + 7 a + 12$ by $(a + 4)$ .

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Solution

We have to evalute, $\frac{a^{2} + 7 a + 12}{(a + 4)}$
Lets factorise $a^{2} + 7 a + 12$
$a^{2} + 7 a + 12$
$= a^{2} + 4 a + 3 a + 12$
$= a (a + 4) + 3 (a + 4)$
$= (a + 4) (a + 3)$
Now,
$\frac{a^{2} + 7 a + 12}{(a + 4)}$
$= \frac{(a + 4) (a + 3)}{(a + 4)}$
$= (a + 3)$
$∴ \frac{a^{2} + 7 a + 12}{(a + 4)} = (a + 3)$

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