Factor polynomial $$ 3a^{3}b+15a^{2}b+2ab+10b $$

$$ 3a^{3}b+15a^{2}b+2ab+10b = b(3a^{2}+2)(a+5) $$

Step 1 :

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

$$ 3a^3b+15a^2b+2ab+10b = b ( 3a^3+15a^2+2a+10 ) $$

Step 2 :

To factor $ 3a^3+15a^2+2a+10 $ we can use factoring by grouping.

Group $ \color{blue}{ 3a^3 }$ with $ \color{blue}{ 15a^2 }$ and $ \color{red}{ 2a }$ with $ \color{red}{ 10 }$ then factor each group.

$$ \begin{aligned} 3a^3+15a^2+2a+10 &= ( \color{blue}{ 3a^3+15a^2 } ) + ( \color{red}{ 2a+10 }) = \\ &= \color{blue}{ 3a^2( a+5 )} + \color{red}{ 2( a+5 ) } = \\ &= (3a^2+2)(a+5) \end{aligned} $$

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