Factor polynomial $$ t^{6}-t^{5}+t^{4}-t^{3} $$
Answer
$$ t^{6}-t^{5}+t^{4}-t^{3} = t^{3}( t^{2}+1 )( t-1 ) $$
Explanation
Step 1 :
After factoring out $ t^{3} $ we have:
$$ t^{6}-t^{5}+t^{4}-t^{3} = t^{3} ( t^{3}-t^{2}+t-1 ) $$Step 2 :
To factor $ t^{3}-t^{2}+t-1 $ we can use factoring by grouping:
Group $ \color{blue}{ x^{3} }$ with $ \color{blue}{ -x^{2} }$ and $ \color{red}{ x }$ with $ \color{red}{ -1 }$ then factor each group.
$$ \begin{aligned} t^{3}-t^{2}+t-1 = ( \color{blue}{ x^{3}-x^{2} } ) + ( \color{red}{ x-1 }) &= \\ &= \color{blue}{ x^{2}( x-1 )} + \color{red}{ 1( x-1 ) } = \\ &= (x^{2}+1)(x-1) \end{aligned} $$This page was created using
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