Factorize of $a^{2} + 10 a + 24$

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Solution

$a^{2} + 10 a + 24$
Split $24$ as such that sum or difference of factor is equal to $10$
$24 = 6 \times 4$
$= 6 + 4 = 10$
$a^{2} + 6 a + 4 a + 24$
$a (a + 6) + 4 (a + 6)$
$= (a + 6) (a + 4)$

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