Factor polynomial $$ 36x^{3}-30x^{2}+60x-50 $$
Answer
$$ 36x^{3}-30x^{2}+60x-50 = 2( 3x^{2}+5 )( 6x-5 ) $$
Explanation
Step 1 :
After factoring out $ 2 $ we have:
$$ 36x^{3}-30x^{2}+60x-50 = 2 ( 18x^{3}-15x^{2}+30x-25 ) $$Step 2 :
To factor $ 18x^{3}-15x^{2}+30x-25 $ we can use factoring by grouping:
Group $ \color{blue}{ 18x^{3} }$ with $ \color{blue}{ -15x^{2} }$ and $ \color{red}{ 30x }$ with $ \color{red}{ -25 }$ then factor each group.
$$ \begin{aligned} 18x^{3}-15x^{2}+30x-25 = ( \color{blue}{ 18x^{3}-15x^{2} } ) + ( \color{red}{ 30x-25 }) &= \\ &= \color{blue}{ 3x^{2}( 6x-5 )} + \color{red}{ 5( 6x-5 ) } = \\ &= (3x^{2}+5)(6x-5) \end{aligned} $$This page was created using
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