Question
Factor polynomial $$ 8x^{4}-32x^{3}-5x^{2}+20x $$
Answer
$$ 8x^{4}-32x^{3}-5x^{2}+20x = x( 8x^{2}-5 )( x-4 ) $$
Explanation
Step 1 :
After factoring out $ x $ we have:
$$ 8x^{4}-32x^{3}-5x^{2}+20x = x ( 8x^{3}-32x^{2}-5x+20 ) $$Step 2 :
To factor $ 8x^{3}-32x^{2}-5x+20 $ we can use factoring by grouping:
Group $ \color{blue}{ 8x^{3} }$ with $ \color{blue}{ -32x^{2} }$ and $ \color{red}{ -5x }$ with $ \color{red}{ 20 }$ then factor each group.
$$ \begin{aligned} 8x^{3}-32x^{2}-5x+20 = ( \color{blue}{ 8x^{3}-32x^{2} } ) + ( \color{red}{ -5x+20 }) &= \\ &= \color{blue}{ 8x^{2}( x-4 )} + \color{red}{ -5( x-4 ) } = \\ &= (8x^{2}-5)(x-4) \end{aligned} $$This page was created using
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