Question
Factor polynomial $$ 6x^{3}+14x^{2}-12x-28 $$
Answer
$$ 6x^{3}+14x^{2}-12x-28 = 2( x^{2}-2 )( 3x+7 ) $$
Explanation
Step 1 :
After factoring out $ 2 $ we have:
$$ 6x^{3}+14x^{2}-12x-28 = 2 ( 3x^{3}+7x^{2}-6x-14 ) $$Step 2 :
To factor $ 3x^{3}+7x^{2}-6x-14 $ we can use factoring by grouping:
Group $ \color{blue}{ 3x^{3} }$ with $ \color{blue}{ 7x^{2} }$ and $ \color{red}{ -6x }$ with $ \color{red}{ -14 }$ then factor each group.
$$ \begin{aligned} 3x^{3}+7x^{2}-6x-14 = ( \color{blue}{ 3x^{3}+7x^{2} } ) + ( \color{red}{ -6x-14 }) &= \\ &= \color{blue}{ x^{2}( 3x+7 )} + \color{red}{ -2( 3x+7 ) } = \\ &= (x^{2}-2)(3x+7) \end{aligned} $$This page was created using
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