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