Question
Factor polynomial $$ 15x^{4}+30x^{3}+18x^{2}+36x $$
Answer
$$ 15x^{4}+30x^{3}+18x^{2}+36x = 3x( 5x^{2}+6 )( x+2 ) $$
Explanation
Step 1 :
After factoring out $ 3x $ we have:
$$ 15x^{4}+30x^{3}+18x^{2}+36x = 3x ( 5x^{3}+10x^{2}+6x+12 ) $$Step 2 :
To factor $ 5x^{3}+10x^{2}+6x+12 $ we can use factoring by grouping:
Group $ \color{blue}{ 5x^{3} }$ with $ \color{blue}{ 10x^{2} }$ and $ \color{red}{ 6x }$ with $ \color{red}{ 12 }$ then factor each group.
$$ \begin{aligned} 5x^{3}+10x^{2}+6x+12 = ( \color{blue}{ 5x^{3}+10x^{2} } ) + ( \color{red}{ 6x+12 }) &= \\ &= \color{blue}{ 5x^{2}( x+2 )} + \color{red}{ 6( x+2 ) } = \\ &= (5x^{2}+6)(x+2) \end{aligned} $$This page was created using
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