Factor polynomial $$ 3x^{4}+9x^{3}+x^{2}+3x $$
Answer
$$ 3x^{4}+9x^{3}+x^{2}+3x = x( 3x^{2}+1 )( x+3 ) $$
Explanation
Step 1 :
After factoring out $ x $ we have:
$$ 3x^{4}+9x^{3}+x^{2}+3x = x ( 3x^{3}+9x^{2}+x+3 ) $$Step 2 :
To factor $ 3x^{3}+9x^{2}+x+3 $ we can use factoring by grouping:
Group $ \color{blue}{ 3x^{3} }$ with $ \color{blue}{ 9x^{2} }$ and $ \color{red}{ x }$ with $ \color{red}{ 3 }$ then factor each group.
$$ \begin{aligned} 3x^{3}+9x^{2}+x+3 = ( \color{blue}{ 3x^{3}+9x^{2} } ) + ( \color{red}{ x+3 }) &= \\ &= \color{blue}{ 3x^{2}( x+3 )} + \color{red}{ 1( x+3 ) } = \\ &= (3x^{2}+1)(x+3) \end{aligned} $$This page was created using
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