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Formula
Factorize the expression
$4ax ^{ 2 } -10ax-24a$
$2 a \left ( x - 4 \right ) \left ( 2 x + 3 \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 4 } \color{#FF6800}{ a } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ a } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 24 } \color{#FF6800}{ a }$
 Tie a common factor 
$\color{#FF6800}{ 2 } \color{#FF6800}{ a } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 12 } \right )$
$2 a \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 12 } \right )$
 Use the factoring formula, $acx^{2} + \left(ad + bc\right)x + bd = \left(ax+b\right)\left(cx+d\right)$
$2 a \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right )$
$2 a \left ( 2 x + 3 \right ) \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right )$
 Expand the expression 
$2 a \left ( 2 x + 3 \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right )$
$2 a \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right )$
 Sort the factors 
$2 a \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right )$
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