Question
Factor polynomial $$ 4x^{4}-x^{3}+20x^{2}-5x $$
Answer
$$ 4x^{4}-x^{3}+20x^{2}-5x = x( x^{2}+5 )( 4x-1 ) $$
Explanation
Step 1 :
After factoring out $ x $ we have:
$$ 4x^{4}-x^{3}+20x^{2}-5x = x ( 4x^{3}-x^{2}+20x-5 ) $$Step 2 :
To factor $ 4x^{3}-x^{2}+20x-5 $ we can use factoring by grouping:
Group $ \color{blue}{ 4x^{3} }$ with $ \color{blue}{ -x^{2} }$ and $ \color{red}{ 20x }$ with $ \color{red}{ -5 }$ then factor each group.
$$ \begin{aligned} 4x^{3}-x^{2}+20x-5 = ( \color{blue}{ 4x^{3}-x^{2} } ) + ( \color{red}{ 20x-5 }) &= \\ &= \color{blue}{ x^{2}( 4x-1 )} + \color{red}{ 5( 4x-1 ) } = \\ &= (x^{2}+5)(4x-1) \end{aligned} $$This page was created using
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