Factor polynomial $$ 3uv-12u+6v-24 $$

$$ 3uv-12u+6v-24 = 3(u+2)(v-4) $$

Step 1 :

Factor out common factor $ \color{blue}{ 3 } $:

$$ 3uv-12u+6v-24 = 3 ( uv-4u+2v-8 ) $$

Step 2 :

To factor $ uv-4u+2v-8 $ we can use factoring by grouping.

Group $ \color{blue}{ uv }$ with $ \color{blue}{ -4u }$ and $ \color{red}{ 2v }$ with $ \color{red}{ -8 }$ then factor each group.

$$ \begin{aligned} uv-4u+2v-8 &= ( \color{blue}{ uv-4u } ) + ( \color{red}{ 2v-8 }) = \\ &= \color{blue}{ u( v-4 )} + \color{red}{ 2( v-4 ) } = \\ &= (u+2)(v-4) \end{aligned} $$

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