Factor polynomial $$ -17x^{3}+5x^{2}+34x-10 $$

$$ -17x^{3}+5x^{2}+34x-10 = -( x^{2}-2 )( 17x-5 ) $$

Step 1 :

After factoring out $ -1 $ we have:

$$ -17x^{3}+5x^{2}+34x-10 = - ~ ( 17x^{3}-5x^{2}-34x+10 ) $$

Step 2 :

To factor $ 17x^{3}-5x^{2}-34x+10 $ we can use factoring by grouping:

Group $ \color{blue}{ 17x^{3} }$ with $ \color{blue}{ -5x^{2} }$ and $ \color{red}{ -34x }$ with $ \color{red}{ 10 }$ then factor each group.

$$ \begin{aligned} 17x^{3}-5x^{2}-34x+10 = ( \color{blue}{ 17x^{3}-5x^{2} } ) + ( \color{red}{ -34x+10 }) &= \\ &= \color{blue}{ x^{2}( 17x-5 )} + \color{red}{ -2( 17x-5 ) } = \\ &= (x^{2}-2)(17x-5) \end{aligned} $$

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