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