Question
Factor polynomial $$ 2x^{3}+18x^{2}+10x+90 $$
Answer
$$ 2x^{3}+18x^{2}+10x+90 = 2( x^{2}+5 )( x+9 ) $$
Explanation
Step 1 :
After factoring out $ 2 $ we have:
$$ 2x^{3}+18x^{2}+10x+90 = 2 ( x^{3}+9x^{2}+5x+45 ) $$Step 2 :
To factor $ x^{3}+9x^{2}+5x+45 $ we can use factoring by grouping:
Group $ \color{blue}{ x^{3} }$ with $ \color{blue}{ 9x^{2} }$ and $ \color{red}{ 5x }$ with $ \color{red}{ 45 }$ then factor each group.
$$ \begin{aligned} x^{3}+9x^{2}+5x+45 = ( \color{blue}{ x^{3}+9x^{2} } ) + ( \color{red}{ 5x+45 }) &= \\ &= \color{blue}{ x^{2}( x+9 )} + \color{red}{ 5( x+9 ) } = \\ &= (x^{2}+5)(x+9) \end{aligned} $$This page was created using
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