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