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