Factor polynomial $$ -10x^{4}-16x^{3}+30x^{2}+48x $$

$$ -10x^{4}-16x^{3}+30x^{2}+48x = ( -2 )x( x^{2}-3 )( 5x+8 ) $$

Step 1 :

After factoring out $ -2x $ we have:

$$ -10x^{4}-16x^{3}+30x^{2}+48x = -2x ( 5x^{3}+8x^{2}-15x-24 ) $$

Step 2 :

To factor $ 5x^{3}+8x^{2}-15x-24 $ we can use factoring by grouping:

Group $ \color{blue}{ 5x^{3} }$ with $ \color{blue}{ 8x^{2} }$ and $ \color{red}{ -15x }$ with $ \color{red}{ -24 }$ then factor each group.

$$ \begin{aligned} 5x^{3}+8x^{2}-15x-24 = ( \color{blue}{ 5x^{3}+8x^{2} } ) + ( \color{red}{ -15x-24 }) &= \\ &= \color{blue}{ x^{2}( 5x+8 )} + \color{red}{ -3( 5x+8 ) } = \\ &= (x^{2}-3)(5x+8) \end{aligned} $$

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