Factor polynomial $$ 30r^{3}-20r^{2}-18r+12 $$
Answer
$$ 30r^{3}-20r^{2}-18r+12 = 2( 5r^{2}-3 )( 3r-2 ) $$
Explanation
Step 1 :
After factoring out $ 2 $ we have:
$$ 30r^{3}-20r^{2}-18r+12 = 2 ( 15r^{3}-10r^{2}-9r+6 ) $$Step 2 :
To factor $ 15r^{3}-10r^{2}-9r+6 $ we can use factoring by grouping:
Group $ \color{blue}{ 15x^{3} }$ with $ \color{blue}{ -10x^{2} }$ and $ \color{red}{ -9x }$ with $ \color{red}{ 6 }$ then factor each group.
$$ \begin{aligned} 15r^{3}-10r^{2}-9r+6 = ( \color{blue}{ 15x^{3}-10x^{2} } ) + ( \color{red}{ -9x+6 }) &= \\ &= \color{blue}{ 5x^{2}( 3x-2 )} + \color{red}{ -3( 3x-2 ) } = \\ &= (5x^{2}-3)(3x-2) \end{aligned} $$This page was created using
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