Factor polynomial $$ 12v^{3}+3v^{2}+24v+6 $$
Answer
$$ 12v^{3}+3v^{2}+24v+6 = 3( v^{2}+2 )( 4v+1 ) $$
Explanation
Step 1 :
After factoring out $ 3 $ we have:
$$ 12v^{3}+3v^{2}+24v+6 = 3 ( 4v^{3}+v^{2}+8v+2 ) $$Step 2 :
To factor $ 4v^{3}+v^{2}+8v+2 $ we can use factoring by grouping:
Group $ \color{blue}{ 4x^{3} }$ with $ \color{blue}{ x^{2} }$ and $ \color{red}{ 8x }$ with $ \color{red}{ 2 }$ then factor each group.
$$ \begin{aligned} 4v^{3}+v^{2}+8v+2 = ( \color{blue}{ 4x^{3}+x^{2} } ) + ( \color{red}{ 8x+2 }) &= \\ &= \color{blue}{ x^{2}( 4x+1 )} + \color{red}{ 2( 4x+1 ) } = \\ &= (x^{2}+2)(4x+1) \end{aligned} $$This page was created using
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