Factor polynomial $$ 98x^{3}yz^{2}+28x^{2}y^{3}z+35xz+10y^{2} $$

$$ 98x^{3}yz^{2}+28x^{2}y^{3}z+35xz+10y^{2} = (14x^{2}yz+5)(7xz+2y^{2}) $$

To factor $ 98x^3yz^2+28x^2y^3z+35xz+10y^2 $ we can use factoring by grouping.

Group $ \color{blue}{ 98x^3yz^2 }$ with $ \color{blue}{ 28x^2y^3z }$ and $ \color{red}{ 35xz }$ with $ \color{red}{ 10y^2 }$ then factor each group.

$$ \begin{aligned} 98x^3yz^2+28x^2y^3z+35xz+10y^2 &= ( \color{blue}{ 98x^3yz^2+28x^2y^3z } ) + ( \color{red}{ 35xz+10y^2 }) = \\ &= \color{blue}{ 14x^2yz( 7xz+2y^2 )} + \color{red}{ 5( 7xz+2y^2 ) } = \\ &= (14x^2yz+5)(7xz+2y^2) \end{aligned} $$

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