#### Factorize x^2+10x+24

Find two numbers with sum = 10 and product = 24.
Clearly such numbers are 6 and 4.
$\therefore \, x^{2}+10x+24=x^{2}+6x+4x+24$

$\therefore \, x(x+6)+4(x+6)=(x+6)(x+4)$

Thus,  $x^{2}+10x+24=(x+6)(x+4)$