Factor polynomial $$ x^{3}+3x^{2}+25x+75 $$
Answer
$$ x^{3}+3x^{2}+25x+75 = ( x^{2}+25 )( x+3 ) $$
Explanation
To factor $ x^{3}+3x^{2}+25x+75 $ we can use factoring by grouping:
Group $ \color{blue}{ x^{3} }$ with $ \color{blue}{ 3x^{2} }$ and $ \color{red}{ 25x }$ with $ \color{red}{ 75 }$ then factor each group.
$$ \begin{aligned} x^{3}+3x^{2}+25x+75 = ( \color{blue}{ x^{3}+3x^{2} } ) + ( \color{red}{ 25x+75 }) &= \\ &= \color{blue}{ x^{2}( x+3 )} + \color{red}{ 25( x+3 ) } = \\ &= (x^{2}+25)(x+3) \end{aligned} $$This page was created using
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