Factor polynomial $$ 12h^{6}+14h^{5}-84h^{4}-98h^{3} $$

$$ 12h^{6}+14h^{5}-84h^{4}-98h^{3} = 2h^{3}( h^{2}-7 )( 6h+7 ) $$

Step 1 :

After factoring out $ 2h^{3} $ we have:

$$ 12h^{6}+14h^{5}-84h^{4}-98h^{3} = 2h^{3} ( 6h^{3}+7h^{2}-42h-49 ) $$

Step 2 :

To factor $ 6h^{3}+7h^{2}-42h-49 $ we can use factoring by grouping:

Group $ \color{blue}{ 6x^{3} }$ with $ \color{blue}{ 7x^{2} }$ and $ \color{red}{ -42x }$ with $ \color{red}{ -49 }$ then factor each group.

$$ \begin{aligned} 6h^{3}+7h^{2}-42h-49 = ( \color{blue}{ 6x^{3}+7x^{2} } ) + ( \color{red}{ -42x-49 }) &= \\ &= \color{blue}{ x^{2}( 6x+7 )} + \color{red}{ -7( 6x+7 ) } = \\ &= (x^{2}-7)(6x+7) \end{aligned} $$

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