Factor polynomial $$ 25x^{3}+25x^{2}-5x-5 $$
Answer
$$ 25x^{3}+25x^{2}-5x-5 = 5( 5x^{2}-1 )( x+1 ) $$
Explanation
Step 1 :
After factoring out $ 5 $ we have:
$$ 25x^{3}+25x^{2}-5x-5 = 5 ( 5x^{3}+5x^{2}-x-1 ) $$Step 2 :
To factor $ 5x^{3}+5x^{2}-x-1 $ we can use factoring by grouping:
Group $ \color{blue}{ 5x^{3} }$ with $ \color{blue}{ 5x^{2} }$ and $ \color{red}{ -x }$ with $ \color{red}{ -1 }$ then factor each group.
$$ \begin{aligned} 5x^{3}+5x^{2}-x-1 = ( \color{blue}{ 5x^{3}+5x^{2} } ) + ( \color{red}{ -x-1 }) &= \\ &= \color{blue}{ 5x^{2}( x+1 )} + \color{red}{ -1( x+1 ) } = \\ &= (5x^{2}-1)(x+1) \end{aligned} $$This page was created using
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