$Divide (a^{2} + 7 a + 10) by (a + 5) .$

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Solution

$Given: \frac{a^{2} + 7 a + 10}{(a + 5)} . . . (i)$

Comparing $a^{2} + 7 a + 10$ with the identity $x^{2} + (a + b) x + a b,$
$we note that, (a + b) = 7 a n d a b = 10$
$S o, 5 + 2 = 7 a n d (5) (2) = 10$

Hence,
$a^{2} + 7 a + 10$
$= a^{2} + 5 a + 2 a + 10$
$= a (a + 5) + 2 (a + 5)$
$= (a + 2) (a + 5)$

From (i), we get
$\frac{a^{2} + 7 a + 10}{(a + 5)} = \frac{(a + 2) (a + 5)}{(a + 5)}$
$= (a + 2)$

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