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