Factor polynomial $$ 30x^{4}+36x^{3}+20x^{2}+24x $$

$$ 30x^{4}+36x^{3}+20x^{2}+24x = 2x( 3x^{2}+2 )( 5x+6 ) $$

Step 1 :

After factoring out $ 2x $ we have:

$$ 30x^{4}+36x^{3}+20x^{2}+24x = 2x ( 15x^{3}+18x^{2}+10x+12 ) $$

Step 2 :

To factor $ 15x^{3}+18x^{2}+10x+12 $ we can use factoring by grouping:

Group $ \color{blue}{ 15x^{3} }$ with $ \color{blue}{ 18x^{2} }$ and $ \color{red}{ 10x }$ with $ \color{red}{ 12 }$ then factor each group.

$$ \begin{aligned} 15x^{3}+18x^{2}+10x+12 = ( \color{blue}{ 15x^{3}+18x^{2} } ) + ( \color{red}{ 10x+12 }) &= \\ &= \color{blue}{ 3x^{2}( 5x+6 )} + \color{red}{ 2( 5x+6 ) } = \\ &= (3x^{2}+2)(5x+6) \end{aligned} $$

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