Question
Factor polynomial $$ 2t^{3}-3t^{2}-6t+9 $$
Answer
$$ 2t^{3}-3t^{2}-6t+9 = ( t^{2}-3 )( 2t-3 ) $$
Explanation
To factor $ 2t^{3}-3t^{2}-6t+9 $ we can use factoring by grouping:
Group $ \color{blue}{ 2x^{3} }$ with $ \color{blue}{ -3x^{2} }$ and $ \color{red}{ -6x }$ with $ \color{red}{ 9 }$ then factor each group.
$$ \begin{aligned} 2t^{3}-3t^{2}-6t+9 = ( \color{blue}{ 2x^{3}-3x^{2} } ) + ( \color{red}{ -6x+9 }) &= \\ &= \color{blue}{ x^{2}( 2x-3 )} + \color{red}{ -3( 2x-3 ) } = \\ &= (x^{2}-3)(2x-3) \end{aligned} $$This page was created using
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