Factor polynomial $$ 3c^{3}+2c^{2}-147c-98 $$

$$ 3c^{3}+2c^{2}-147c-98 = ( c-7 )( c+7 )( 3c+2 ) $$

Step 1 :

To factor $ 3c^{3}+2c^{2}-147c-98 $ we can use factoring by grouping:

Group $ \color{blue}{ 3x^{3} }$ with $ \color{blue}{ 2x^{2} }$ and $ \color{red}{ -147x }$ with $ \color{red}{ -98 }$ then factor each group.

$$ \begin{aligned} 3c^{3}+2c^{2}-147c-98 = ( \color{blue}{ 3x^{3}+2x^{2} } ) + ( \color{red}{ -147x-98 }) &= \\ &= \color{blue}{ x^{2}( 3x+2 )} + \color{red}{ -49( 3x+2 ) } = \\ &= (x^{2}-49)(3x+2) \end{aligned} $$

Step 2 :

Rewrite $ c^{2}-49 $ as:

$$ c^{2}-49 = (c)^2 - (7)^2 $$

Now we can apply the difference of squares formula.

$$ I^2 - II^2 = (I - II)(I + II) $$

After putting $ I = c $ and $ II = 7 $ , we have:

$$ c^{2}-49 = (c)^2 - (7)^2 = ( c-7 ) ( c+7 ) $$

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