Factor polynomial $$ 10xyz+10xy-5xz-5x $$

$$ 10xyz+10xy-5xz-5x = 5x(2y-1)(z+1) $$

Step 1 :

Factor out common factor $ \color{blue}{ 5x } $:

$$ 10xyz+10xy-5xz-5x = 5x ( 2yz+2y-z-1 ) $$

Step 2 :

To factor $ 2yz+2y-z-1 $ we can use factoring by grouping.

Group $ \color{blue}{ 2yz }$ with $ \color{blue}{ 2y }$ and $ \color{red}{ -z }$ with $ \color{red}{ -1 }$ then factor each group.

$$ \begin{aligned} 2yz+2y-z-1 &= ( \color{blue}{ 2yz+2y } ) + ( \color{red}{ -z-1 }) = \\ &= \color{blue}{ 2y( z+1 )} \color{red}{ -1( z+1 ) } = \\ &= (2y-1)(z+1) \end{aligned} $$

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