Question
Factor polynomial $$ x^{6}+2x^{4}+x^{2}+2 $$
Answer
$$ x^{6}+2x^{4}+x^{2}+2 = ( x^{4}+1 )( x^{2}+2 ) $$
Explanation
To factor $ x^{6}+2x^{4}+x^{2}+2 $ we can use factoring by grouping:
Group $ \color{blue}{ x^{6} }$ with $ \color{blue}{ 2x^{4} }$ and $ \color{red}{ x^{2} }$ with $ \color{red}{ 2 }$ then factor each group.
$$ \begin{aligned} x^{6}+2x^{4}+x^{2}+2 = ( \color{blue}{ x^{6}+2x^{4} } ) + ( \color{red}{ x^{2}+2 }) &= \\ &= \color{blue}{ x^{4}( x^{2}+2 )} + \color{red}{ 1( x^{2}+2 ) } = \\ &= (x^{4}+1)(x^{2}+2) \end{aligned} $$This page was created using
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