Question
Factor polynomial $$ 10qr^{3}+20qr^{2}+2r^{3}+4r^{2} $$
Answer
$$ 10qr^{3}+20qr^{2}+2r^{3}+4r^{2} = 2r^{2}(5q+1)(r+2) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 2r^2 } $:
$$ 10qr^3+20qr^2+2r^3+4r^2 = 2r^2 ( 5qr+10q+r+2 ) $$Step 2 :
To factor $ 5qr+10q+r+2 $ we can use factoring by grouping.
Group $ \color{blue}{ 5qr }$ with $ \color{blue}{ 10q }$ and $ \color{red}{ r }$ with $ \color{red}{ 2 }$ then factor each group.
$$ \begin{aligned} 5qr+10q+r+2 &= ( \color{blue}{ 5qr+10q } ) + ( \color{red}{ r+2 }) = \\ &= \color{blue}{ 5q( r+2 )} + \color{red}{ 1( r+2 ) } = \\ &= (5q+1)(r+2) \end{aligned} $$This page was created using
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