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