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