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