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