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