Factor polynomial $$ 12h^{5}+16h^{4}+6h^{3}+8h^{2} $$
Answer
$$ 12h^{5}+16h^{4}+6h^{3}+8h^{2} = 2h^{2}( 2h^{2}+1 )( 3h+4 ) $$
Explanation
Step 1 :
After factoring out $ 2h^{2} $ we have:
$$ 12h^{5}+16h^{4}+6h^{3}+8h^{2} = 2h^{2} ( 6h^{3}+8h^{2}+3h+4 ) $$Step 2 :
To factor $ 6h^{3}+8h^{2}+3h+4 $ we can use factoring by grouping:
Group $ \color{blue}{ 6x^{3} }$ with $ \color{blue}{ 8x^{2} }$ and $ \color{red}{ 3x }$ with $ \color{red}{ 4 }$ then factor each group.
$$ \begin{aligned} 6h^{3}+8h^{2}+3h+4 = ( \color{blue}{ 6x^{3}+8x^{2} } ) + ( \color{red}{ 3x+4 }) &= \\ &= \color{blue}{ 2x^{2}( 3x+4 )} + \color{red}{ 1( 3x+4 ) } = \\ &= (2x^{2}+1)(3x+4) \end{aligned} $$This page was created using
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