Factor polynomial $$ 3n^{3}+7n^{2}+18n+42 $$
Answer
$$ 3n^{3}+7n^{2}+18n+42 = ( n^{2}+6 )( 3n+7 ) $$
Explanation
To factor $ 3n^{3}+7n^{2}+18n+42 $ we can use factoring by grouping:
Group $ \color{blue}{ 3x^{3} }$ with $ \color{blue}{ 7x^{2} }$ and $ \color{red}{ 18x }$ with $ \color{red}{ 42 }$ then factor each group.
$$ \begin{aligned} 3n^{3}+7n^{2}+18n+42 = ( \color{blue}{ 3x^{3}+7x^{2} } ) + ( \color{red}{ 18x+42 }) &= \\ &= \color{blue}{ x^{2}( 3x+7 )} + \color{red}{ 6( 3x+7 ) } = \\ &= (x^{2}+6)(3x+7) \end{aligned} $$This page was created using
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