Question
Factor polynomial $$ 20v^{4}-40v^{3}-2v^{2}+4v $$
Answer
$$ 20v^{4}-40v^{3}-2v^{2}+4v = 2v( 10v^{2}-1 )( v-2 ) $$
Explanation
Step 1 :
After factoring out $ 2v $ we have:
$$ 20v^{4}-40v^{3}-2v^{2}+4v = 2v ( 10v^{3}-20v^{2}-v+2 ) $$Step 2 :
To factor $ 10v^{3}-20v^{2}-v+2 $ we can use factoring by grouping:
Group $ \color{blue}{ 10x^{3} }$ with $ \color{blue}{ -20x^{2} }$ and $ \color{red}{ -x }$ with $ \color{red}{ 2 }$ then factor each group.
$$ \begin{aligned} 10v^{3}-20v^{2}-v+2 = ( \color{blue}{ 10x^{3}-20x^{2} } ) + ( \color{red}{ -x+2 }) &= \\ &= \color{blue}{ 10x^{2}( x-2 )} + \color{red}{ -1( x-2 ) } = \\ &= (10x^{2}-1)(x-2) \end{aligned} $$This page was created using
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